Modeling of microcrack formation in orthogonal machining

International Journal of Machine Tools & Manufacture 80-81 (2014) 18–29

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International Journal of Machine Tools & Manufacture journal homepage: www.elsevier.com/locate/ijmactool

Modeling of microcrack formation in orthogonal machining Dattatraya Parle a,1, Ramesh K. Singh a, Suhas S. Joshi a,n, G.V.V. Ravikumar b a b

Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India Engineering Services, Infosys Limited, Bangalore 560100, India

art ic l e i nf o

a b s t r a c t

Article history: Received 9 November 2013 Received in revised form 9 February 2014 Accepted 10 February 2014 Available online 6 March 2014

Researchers have observed formation of microcracks during metal cutting and attributed their occurrence to various phenomena. Shaw postulated that under the combined shear and normal stress conditions on shear plane, microcracks could occur when strain in the shear plane exceeds the failure limit of material. However, the phenomenon of microcrack formation is difficult to capture experimentally. Therefore, this paper presents a finite element (FE) model to simulate the microcrack formation during orthogonal cutting. The model has been validated by performing orthogonal micro-cutting experiments and error in cutting force prediction is less than 11.5%. The simulation helps identify locations at which microcracks are formed in the shear zone using the mathematical and FEA models. Furthermore, the contribution of the specific energy (energy/volume) associated with the microcrack formation to the total specific energy of the shear zone has been evaluated. Contribution of microcracks to specific shear zone energy is found to be in the range of 0–20% for AISI 1215 and 0–15% for AISI 1045 under different machining conditions. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Orthogonal cutting Specific shear zone energy Microcracks Finite element analysis

1. Introduction Machining involves removal of work material normally with some kind of fracture. The fracture can be of varied dimensions and occurs at various locations in machining zones. Normally, gross and distributed type micro-fractures are observed in machining. In the past, these fractures have been studied and modeled by various researchers. Gross fracture formation is known to occur even in ductile metals under certain cutting conditions and work material properties [1]. The cutting mechanism in ceramics was modeled by considering the propagation of small and sharp flaws (i.e., cracks) using the concept of fracture mechanics by Iwata and Ueda [2,3] and also analytically by Percy and Ueda [4]. Turkovich and Field [5] and Kluft et al. [6] showed that crack formation and its propagation during machining affect several aspects such as chip formation mechanism, cutting forces and machine surface integrity. Recently, analytical and numerical models for gross fracture formation in machining have been proposed by Atkins [7,8] and Subbiah and Melkote [1], respectively, in machining of ductile materials. Atkins [7,8] used fracture toughness to estimate the amount of energy consumed in material separation during the

n

Corresponding author. Tel.: þ 91 22 2576 7527; fax: þ 91 22 2572 6675. E-mail address: [email protected] (S.S. Joshi). 1 Working at Engineering Services, Infosys Ltd., Pune, India.

http://dx.doi.org/10.1016/j.ijmachtools.2014.02.003 0890-6955 & 2014 Elsevier Ltd. All rights reserved.

chip formation in machining. Subbiah and Melkote [1] presented an approach to model the metal cutting that captures ductile fracture leading to material separation using the FEA. Madhavan et al. [9] reported chip formation as an indentation process which is considered to be a result of occurrence of brittle/ductile fracture just ahead of the tool. Other researchers have investigated the occurrence of microcracks or their accumulation leading to gross fracture along the shear zone during metal cutting. Komanduri and Brown [10] have experimentally shown the presence of microcracks in machining of low carbon steel and other ductile materials. The microcracks (or smaller voids) tend to disappear after unloading of the chip and hence, the size and the number of microcracks observed in the shear plane were not very accurate. Zhang and Bagchi [11] observed that micro-fracture during chip separation occurs by nucleation of voids in the vicinity of the tool tip. Iwata and Ueda [2] have observed mechanism of microcracks (flaws) growth to form a gross fracture in machining of ceramics. They have studied dynamic behavior of cracks in shear zone within the framework of fracture mechanics during machining. Luong [12] reported presence of microcracks during their experiments on specimen subjected to a loading similar to shear plane during metal cutting. But the quantification of density of microcracks was difficult on chip as reported by Komanduri and Brown [10]. In a pioneering work, Shaw [13] suggested that under the influence of unusually high shear stress and shear strain conditions in machining, localized fracture in the form of microcrack formation takes place

D. Parle et al. / International Journal of Machine Tools & Manufacture 80-81 (2014) 18–29

Nomenclature ALE CDM CCD FEA OMM SPH A, B, C,

arbitrary Lagrangian–Eulerian central difference method charge coupled device finite element analysis on machine measurement smoothed-particle hydrodynamics n, and m Johnson–Cook constant parameters for specified material C1 and C2 material constants Cd damping co-efficient matrix Fc cutting force E Young's modulus of elasticity IEn internal energy of nth time step K stiffness matrix M mass matrix P internal force R2 co-efficient of determination T melt melting temperature of the material T room room temperature of the material V cutting speed

along the shear plane. Discontinuous microcracks usually get initiated on the shear plane in the form of localized fracture (i.e., microcrack) during chip formation. In general, microcracks have been used to explain several aspects of material behavior during machining such as, chip segmentation process [2], microcrack coalescence process in the vicinity of the tool tip [14], and the negative work hardening phenomenon observed due to microcracks in machining [15]. Shaw [16] also suggested that microcrack formation could contribute substantially to specific cutting energy (i.e., size effect) in metal cutting. Although, the gross fracture phenomenon ahead of the tool has been modeled to some extent, the formation of microcracks along shear zone during machining has not been modeled. This study focuses on understanding of the microcrack formation and its role in specific shear zone energy in metal cutting via numerical simulation. The study is based on the theory of microcrack formation in the deformation zone during the machining of ductile materials proposed by Shaw [13]. The theory postulated that shear stress and strain in metal cutting are unusually high and the discontinuous microcracks are usually formed on the shear plane. If the material being cut is brittle or compressive stresses on the shear plane are relatively low, microcracks grow into gross cracks thereby giving rise to discontinuous chip formation. However, the theory also suggests that the microcracks do get suppressed during the machining process and their number keeps varying in the process based on the cutting conditions. Moreover, literature reports [10,12,13], it is not possible to measure exact size and number of microcracks in shear zone during experiments on cutting due to their small size and unloading effect of quick-stop mechanism. In literature, there is no specific analytical or numerical formulation to estimate the number, the location and the contribution of the microcracks to specific shear zone energy during chip formation. Therefore, the objective of this study is to model microcrack formation in the shear zone during chip formation as postulated by Shaw [13] using framework of finite element analysis (FEA). The work presented in this paper uses the failure criteria suggested by Shaw to identify the location or the elements (in finite element model) undergoing failure. These locations correspond to the location of microcrack formation in shear zone. Thus, knowing the number of

19

Velement element volume f feed c wave propagation speed l minimum element edge length Δt time step Δtcritical critical time step u displacement u_ velocity u€ acceleration U sMicrocrack specific microcrack energy U sShearZone specific shear zone energy εfailure failure strain in shear zone εp effective plastic strain value ε_ p non-dimensional plastic strain rate ε_ 0 η triaxiality parameter s normal stress on shear zone sm hydrostatic mean stress s equivalent stress τ shear stress of shear zone γ rake angle ν Poisson's ratio

microcracks, their contribution in specific shear zone energy has been quantified as a function of processing parameters. In the first section of this paper, the theory of microcrack formation in metal cutting is briefly explained followed by finite element analysis to identify and evaluate the number of failed elements referred to as microcracks during chip formation in the shear zone. The FEA model has been benchmarked with the experimental results. Finally, the contribution of microcracks to specific shear zone energy has been evaluated by comparing specific energy of the microcracks with the specific energy of shear zone in metal cutting.

2. Modeling of microcrack formation in machining To model the microcrack formation in machining and to evaluate the contribution of microcracks in the specific energy of shear zone, the procedure shown in Fig. 1 has been used.

Evaluation of failure strain criteria (Shaw’s Hypothesis)

Structural-Thermal FE analysis of orthogonal cutting using LSDYNA

Experimental validation of FE simulations

Post-processing of stress, strain, temperature and cutting forces

Evaluating the strain failure criteria to locate failed elements i.e. microcracks in shear zone

Evaluation of contribution of microcracks to specific shear zone energy Fig. 1. Flow chart for modeling and contribution evaluation of microcracks in micro-cutting.

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D. Parle et al. / International Journal of Machine Tools & Manufacture 80-81 (2014) 18–29

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  1 2 s¼ s þ 3τ 2 2

2.1. Evaluation of failure criteria for microcrack formation The failure criterion is based on Shaw's hypothesis of microcrack formation [13]. Shaw performed experiments using combined axial, compression and torsion loads to mimic the multiaxial state of stress that exists on the shear plane. The material used in their study was low carbon steel i.e., AISI 1215 steel. The results of these experiments show that the failure strain increases as the compressive stress on the shear plane increases as shown in Fig. 2. The failure strain of material is low when normal stress on the shear plane is low. This phenomenon of microcracks formation resembles internal necking or localized necking. It may be noted that this localized criterion is different from the material separation criterion generally used for modeling of chip formation during FE simulations. As per the Shaw's hypothesis, these microcracks may or may not lead to formation of gross fracture or chip separation depending upon the stress state in the shear zone. Nevertheless, the microcrack formation contributes significantly to the specific shear zone energy and hence the size-effect. Fig. 2 shows that a downward trend observed in the shear stress beyond a certain value of strain is due to a gradual increase in the unsound internal area corresponding to microcracks formation. Shaw [13] proposed that the localized microcracks or voids will form along the shear plane, at a critical value of strain depending on the ductility of the material. If the compressive stress on the shear plane is too high, the formation of microcracks will either be postponed to unusually high values of strain or likely to lead to rewelding of microcracks. In this work, the above mentioned hypothesis is used to formulate an empirical model for AISI 1215 steel that captures shear stress vs. normal strain behavior shown in Fig. 2. The failure strain (εfailure) is a function of shear and normal stresses. A phenomenological model has been formulated empirically by fitting an exponential equation (see Eq. (1)) to the data in Fig. 2 for AISI 1215 steel using a MATLAB routine as given below

εfailure ¼ 0:6254e  7:01η

ð1Þ

where

η¼

sm s

ð2Þ

1 3

ð3Þ

sm ¼ s 600

Using Eq. (1), the failure strains are predicted, knowing the values of shear and normal stresses on the shear plane under various machining conditions (see Fig. 3). It is observed that the prediction is within 97% (R2 ¼0.97) of confidence limit. Literature [17–19] also reveals that ductile fracture of metals occurs as a result of nucleation and growth of microscopic voids. The main parameters that influence void nucleation and growth are the triaxiality factor and the plastic strain. Hence, failure model for microcrack formation is evaluated in terms of triaxiality parameter using Shaw's [13] experimental data. Rice and Tracey [18] also explained ductile growth and coalescence of microscopic voids under the superposition of hydrostatic stresses using the following equation:

εfailure ¼ C 1 eC 2 η

ð5Þ

where C1 and C2 are the material constants determined experimentally. Material under triaxial stress state begins to develop microscopic voids. Shear zone in metal cutting is also subjected to similar stress state i.e., mainly shear and normal stress. Due to this kind of stress state, microcracks initiate in a progressive way within shear zone. 2.2. Finite element modeling for microcrack formation in machining In this work, the FE modeling approach has been used to identify the work elements subjected to εfailure (Eq. (1)) in shear zone. These elements have been considered to be the locations at which microcrack formation takes place. As mentioned in Fig. 1, the approach uses structural–thermal analysis in the framework of LS-DYNA software. The FE analysis involves pure Lagrangian approach with adaptive re-meshing. 2.2.1. Geometry, meshing, boundary conditions and process parameters In this work, orthogonal cutting and a corresponding 2D geometrical model have been considered. FE modeling was done in the area close to the cutting edge of the tool for micro-cutting simulations. Workpiece and tool geometry were kept as small as possible to reduce computational efforts but without compromising outcome of the simulations. A length of 2 mm of the workpiece was seen to be enough to capture cutting mechanics and chip formation during micro-cutting simulations. Similarly, height of workpiece was limited to 1 mm as maximum uncut chip thickness was 100 μm, which was sufficiently large to study shear zone area ahead of tool tip and cutting width on workpiece was kept

500

600

400

500 Shear Stress (MPa)

Shear Stress, (MPa)

ð4Þ

300

200

.O

100

400 300 200 Experimental failure strain from Ref. [13] 100

Failure strain predicted using Eq. 1

0 0

0.5

1 Normal Strain,

1.5

2

Fig. 2. Shear stress vs. strain results in combined compression shear test for AISI 1215 [13].

0 0.0

0.5

1.0

1.5

2.0

2.5

Failure Strain Fig. 3. Failure strain vs. shear stress at various normal stress (s) levels.

D. Parle et al. / International Journal of Machine Tools & Manufacture 80-81 (2014) 18–29

2.2.2. Material model for tool and workpiece The cutting tool was modeled as a rigid body, whereas the workpiece was modeled as an elasto-plastic body. Table 2 shows overall tool and work material properties used in this FE simulation of orthogonal cutting. Elasto-plastic behavior of workpiece material was modeled using Johnson–Cook (J–C) [20] constitutive material model and is Table 1 Process parameters for simulations of orthogonal cutting. Cutting speeda (m/min) Rake angle (deg) Clearance angle (deg) Feed (μm) Tool edge radius (μm) Tool width (mm) Friction model Static friction coefficient Dynamic friction coefficient Initial gap between workpiece and tool (μm) Dry cutting initial temperature (1C)

1, 2, 3, 4  5, 0, 5, 10 5 25, 50, 75, 100 Up-sharp, 25, 50, 75 1 Coulomb friction 0.21 0.14 10 35

a Additional simulations were performed at higher cutting speeds of 25 m/min and 50 m/min, 51 rake angle, 75 μm feed and up-sharp tool on AISI 1215.

Tool Cutting Speed

Contact Definition

Workpiece

u =u =0

Fig. 4. 2D FE model of orthogonal cutting.

Table 2 Material properties for tool and workpiece. Properties

Tool

Workpiece

Material

Tungsten carbide

AISI 1215

Mechanical properties Density (kg/m3) Young's modulus (MPa) Poisson's ratio

15,800 680,000 0.24

7780 200,000 0.29

Thermal properties Thermal conductivity (W/m 1C) Heat capacity (J/kg 1C) Melting temperature (1C) Thermal expansion co-efficient (m/m1C)

84 200 2870 0.0000056

51.9 472 1400 0.000012

500 400 Stress (MPa)

0.2 mm. The cutting tool used has rake angle between  51 and 101 (see Table 1) and clearance angle of 51. Fully integrated quadrilateral shell elements, with plain strain formulations have been used for coupled structural–thermal analysis. Fig. 4 shows the meshed model. Mesh convergence was performed before finalizing the mesh size and converged mesh size of 10 μm was used in the present work for meshing of workpiece and tool. To establish proper contact between surfaces of a rigid body (tool) and a deformable body (workpiece), meshing of the tool was carried out using same element size. The workpiece was constrained along X- and Y-directions i.e., at its bottom edge as shown in Fig. 4. The cutting speed was given to the tool in the X-direction, see Fig. 4. The contact between the workpiece and the tool was defined to include the frictional and thermal effects as mentioned in Table 1. However, sticking phenomenon was not considered in the friction model. In the deformation zone near the tool point, severe element distortion was observed due to high strains, hence, adaptive re-meshing has been used. Table 1 shows overall process parameters used in the FE simulation of orthogonal machining. In this analysis, the effect of cutting fluid has not been considered. Four levels of parameters were chosen to capture the non-linearity in the trends, if any.

21

-3 -1

Strain Rate = 2×10 s Temperature = 45 °C

300 Experimental Stress-Strain [21] Predicted using Eq. 5

200 100 0 0.00

0.10

0.20

0.30

Strain Fig. 5. Stress vs. strain plot for AISI 1215 steel.

given as follows:   p   m    ε_ T T room 1 s ¼ A þBðεp Þn 1 þ C ln _ ε0 T melt  T room

ð6Þ

The stress vs. strain data for AISI 1215 steel was obtained from Hwang and Wang's [21] experimental tests. Fig. 5 shows only a representative experimental curve, and its comparison with the J–C model obtained using the entire experimental data from Ref. [21]. The experiments were conducted under a constant strain rate of 2  10  3 s  1 at various temperatures. J–C parameters A¼350.3 MPa, B¼325.8 MPa, C¼0.04, n¼0.9 and m¼ 0.3 has been obtained from experimental data shown in Fig. 5 using a multi-objective optimization program in MATLAB. J–C parameters obtained were predicted within 99% (R2 ¼0.99) of confidence limit. 2.2.3. Chip separation criteria A chip separation criterion in numerical models of metal cutting is one of the critical aspects to generate appropriate types of chips. Some of the commonly employed chip separation techniques are node separation, element deletion and pure deformation during metal cutting FE simulations [22]. Recently, Asad et al. [23] have employed fracture energy-based damage criteria for chip formation during metal cutting simulation using Abaqus. Mabrouki et al. [24] presented numerical and experimental methodology employing material damage and fracture energy-based physical phenomena of chip formation in orthogonal cutting. Pure deformation technique with adaptive re-meshing is popular and commonly employed by various researchers [25,26] for chip formation during metal cutting simulations. As tool advances, severely deformed elements of workpiece in the shear zone are re-meshed to a more regular in shaped elements. The work material element that overlaps with the tool is removed as chip during the re-meshing. The present work employs pure deformation-based criteria with adaptive re-meshing

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D. Parle et al. / International Journal of Machine Tools & Manufacture 80-81 (2014) 18–29

for chip formation during metal cutting simulations in the framework of LS-DYNA. 2.2.4. Numerical formulations The FE simulation of metal cutting requires dynamic non-linear numerical formulation. This work uses explicit integration method to evaluate results. The explicit simulations using LS-DYNA [27] use four methods such as Lagrangian, Eulerian, arbitrary Lagrangian–Eulerian (ALE) and smoothed-particle hydrodynamics (SPH). As metal cutting process is a large deformation and dynamic problem, the Lagrangian formulation has been used in this simulation. The governing discretized FEA equation to obtain a time dependent solution of displacement, at time step tn, is given by the following equation [26]: M u€ n þ C d u_ n þ Kun ¼ P n

ð7Þ

Eq. (7) can be solved using central difference method (CDM) as given below     1 Δt M þ ΔtC d un þ 1 ¼ Δt 2 P n  ðΔt 2 K 2MÞun  M  C d un  1 2 2 ð8Þ where un þ 1 ¼ un  Δt u_ n þ

Δt 2 € 2

un

ð9Þ

The solution of CDM is conditionally stable, i.e., the size of the time step is limited. Hence, critical time step, Δtcritical is calculated as below, and has been used in this simulation

Δt critical ¼

l c

ð10Þ

where l¼minimum element edge length and c¼wave propagation speed. Using the above formulation, the FE simulation in LS-DYNA computes internal energy (IE) of an element based on the six components of stresses and strains. The computation is done incrementally for each element as given by the following equation: IEn þ 1 ¼ IEn þ Σsij εij V element

ð11Þ

To evaluate the total internal energy of shear zone, the internal energies of each element in this shear zone has been added.

Similarly, the internal energy of microcracks has been evaluated by adding the total internal energies of the failed elements. These internal energies have been further used to evaluate contribution of microcracks towards specific shear zone energies in metal cutting. The specific shear zone energy has been computed by dividing the internal energy with the volume of the thick shear zone. 2.2.5. Post-processing of FEA results In the post-processing of FE simulation, the state variables and machining results, such as stress, strain, shear angle, temperatures, cutting force, etc. have been evaluated. These results have been presented in Section 3. Results have also been used to evaluate specific shear zone energy in orthogonal cutting for various orthogonal machining conditions. The machining parameters used in this simulation are cutting speed, rake angle and feed, see Table 1 for levels of these parameters. 2.3. Experimental validation of FEA simulations The validation of FEA simulation involves a comparison of cutting force obtained from the FE simulation with those obtained from the experimental results. The experiments were carried out on a three-axis multipurpose miniature machine tool developed by Mikrotools [28] for high precision micromachining. Fig. 6a shows experimental setup used in this work. This micro-machine has 70.1 μm positioning resolution and 1 μm accuracy. Micro-cutting experiments on low carbon steel (AISI 1215) and medium carbon steel (AISI 1045) were undertaken using a fullfactorial experimental design. Table 3 shows the levels and factors which were used in the micro-cutting experiments. Four levels of rake angle, four levels of feed and three levels of cutting speed were selected. Due to constraints imposed by the machine, the experiments could be performed at the cutting speeds varying between 1 and 3 m/min. A full-factorial design yields 48 runs (for each material). One half of the total experiments were repeated under various parametric conditions. Cutting operation was performed by replacing spindle head by a tool holder. Cutting tool is in the form of triangular inserts from Tungaloy. The inserts were made of tungsten carbide and were mounted in an insert holder (Fig. 6b). To ensure that cutting edges

Fig. 6. Orthogonal cutting experimental setup details.

D. Parle et al. / International Journal of Machine Tools & Manufacture 80-81 (2014) 18–29

35

Table 3 Factors and their levels during micro-cutting experiments on AISI 1215 and AISI 1045. Rake angle (deg)

Feed (μm)

Cutting speed (m/min)

0 1 2 3

5 0 5 10

25 50 75 100

1 2 3 –

30 Cutting Force (N)

Level

23

25 20 15 10

Experiments FEA Simulation

5 0 0

0.1

0.2

0.3

Time (s) Fig. 8. Cutting force vs. time. (Process parameters: V ¼ 3 m/min, γ¼ 51, f¼ 75 μm, Tool-Up sharp.)

Fig. 7. Image of chip formation obtained using camera.

remain reasonably sharp during each experiment, each cutting edge was used for performing only six cuts (experiments). Four different insert holders were manufactured to adjust rake angle of the cutting tool. Workpiece was mounted on a three-component dynamometer (Kistler Minidyne 9256C2) using a workpiece holder (Fig. 6c). The workpiece configuration and dimensions are depicted in a photograph shown in Fig. 6d. The workpiece has 24 ridges, each of width 0.2 mm, height 1.5 mm and separated by 1 mm see Fig. 6d. The ridges were fabricated using wire-EDM. Width of each ridge was measured at three locations i.e., top, middle and bottom using a profilometer. An average error in the cutting width does not exceed 4%. Before performing experiments, each workpiece was cleaned using Turpentine and subjected to ultrasonic bath for 30 min. A CCD-based OMM camera was used to monitor orthogonal cutting experiments. Fig. 7 shows typical image of chip formation during the orthogonal cutting obtained using the camera. Inset image shows a sketch of the orthogonal cutting. A typical distribution of cutting force vs. time obtained from the FE simulations and the experiments is shown in Fig. 8. The forces show an initial unsteady region followed by a steady-state region. There are peaks and valleys of small magnitude in the steady-state as well. This is due to behavior of the numerical as well as measurement system and does not refer to physical phenomena in orthogonal cutting. Minimum, maximum and average cutting forces in the steady-state region are 16.65 N, 30.65 N and 23.18 N, respectively with a standard deviation of 3.62 N in the experimental results. Similarly, average cutting force in the steady-state region for FEA simulations is 24.58 N. Error in FEA simulation and experimental average cutting force is 5.69% for given cutting conditions. Moreover, overall % error does not exceed 11.50%. Hence, it was concluded that the procedure adopted in this work is fairly accurate.

zone is 1177.50 MPa for a typical case shown in Fig. 9a. A round form like fillet appears at the beginning of the cutting simulation. It is caused due to adaptive re-meshing during simulation. Elements in the beginning of workpiece take round shape after re-meshing during chip separation. The stresses are nearly uniform along the shear plane. The shear plane appears as a thick zone referred to as shear zone. The shear angle is evaluated by knowing nodal co-ordinates at point A, B and C as shown in Fig. 9b and c. For a sharp tool, the point A is considered to be the tool tip. However, for a rounded edge tool, the point A lies at the center of cutting edge radius. At the same time, the other end of shear plane is considered to be at the point B where chip changes its direction on workpiece, usually this occurs within an element. Typical strain, strain rate and temperature plots obtained using FEA simulations are shown in Fig. 10. The machining strains are found to be in the range of 1–3.5 as shown in Fig. 10a. The strain rates are found to be in between 1000 and 4270 s  1 as shown in Fig. 10b. Similarly, a temperature plot obtained shows that the temperature in the contact region is higher than that of in the other regions. The maximum temperature observed is 106.5 1C for a typical case, see Fig. 10c. 3.2. Cutting forces A variation of cutting forces with the machining parameters like cutting speed, rake angle and feed is illustrated in Fig. 11a–d. It is observed that cutting forces increase with an increase in feed (see Fig. 11a) and tool edge radius (see Fig. 11d), whereas the forces decrease with an increase in the cutting speed (see Fig. 11b) and rake angle (see Fig. 11c). The results of additional simulations carried out at higher cutting speed of 25 m/min and 50 m/min are in line with these results and are presented in Appendix A. Results of cutting forces are in agreement with the fundamental machining behavior of ductile materials [29]. Further, a straight line is fitted to the plot of cutting forces vs. feed as shown in Fig. 11a. It is observed that the extension of this line (dotted line) has þve intercept along Y-axis. The presence of þve intercept at zero feed indicates that there is a constant component of force involved in material separation and could potentially be correlated with the fracture component as suggested by Atkins [7].

3. Results and discussions 3.1. State variables and shear angle A typical von-Mises (VM) stress contour plot obtained by the FEA simulation is shown in Fig. 9. The plot shows three distinct deformation zones; shear zone, tool–chip interface and newly machined surface. The maximum von-Mises stress in the shear

4. Identification of microcracks and their contribution to specific shear zone energy 4.1. Identification of microcracks In order to identify microcracks (i.e., locations of the failed element) along the shear zone in orthogonal cutting, the plastic

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D. Parle et al. / International Journal of Machine Tools & Manufacture 80-81 (2014) 18–29

B φ

C

Shear zone

A

Tool-chip interface

Tool B φ

C

A

Workpiece Fig. 9. (a) von-Mises stress plots showing different zones; (b) shear angle evaluation for up-sharp tools; and (c) shear angle evaluation for tools with rounded edge. (Process parameters: V ¼3 m/min, γ ¼51, f¼ 75 μm, Tool-Up sharp.)

Fig. 10. (a) Plastic strain distribution; (b) strain rate distribution; and (c) temperature distribution in various zones of orthogonal cutting. (Process parameters: V ¼3 m/min, γ ¼51, f¼ 75 μm, Tool-Up sharp.)

strains due to multi-axial loading have been evaluated for each element in a thick shear zone using the FE simulations. The magnitude of this strain is compared with the failure strain given by Eq. (1). An element in the shear zone is considered to be failed if the plastic strain on it exceeds the failure strain given by Eq. (1). Typical locations of such failed elements are shown in Fig. 12a–d. These failed elements are referred to as microcracks in the present study. According to Shaw's hypothesis, microcracks appear within the thick shear zone as shown in Fig. 12. In this study, up to 8 microcracks

were observed during micro-cutting of low carbon steel based on cutting conditions. Similarly, Komanduri [10] and Luong [12] reported 0–6 microcracks in the shear zone of metal cutting during cutting experiments. However, Shaw [13] stated that smaller microcracks would tend to disappear due to induced unloading of the chip in the quick-stop procedure. Therefore, the size and number of microcracks observed are not thought to be very accurate using experimental approach. Hence, numerical modeling-based approach has been adopted in the present study to identify microcracks more accurately and quantify their contribution to the specific shear zone energy.

Cutting Force (N)

D. Parle et al. / International Journal of Machine Tools & Manufacture 80-81 (2014) 18–29

35 30.92 30 24.58 25 20 17.58 15 10.2 10 V=3 m/min, =5 deg 5 Tool = Up sharp 0 25 50 75 100 Feed (micrometer)

27.11

25.99 24.58

28.5 24.07

f=75 m, =5 deg Tool = Up sharp 1

2

3

4

Cutting speed (m/min)

27.08

24.58 21.77

24.58

26.57

28.9

25

30.45

V=3 m/min, f=75 m Tool = Up sharp

V=3 m/min, f=75 m =5 deg

-5

0

0

5

10

Rake angle (deg.)

25

50

75

Tool edge radius (micrometer)

Fig. 11. Cutting force vs. (a) feed, (b) cutting speed, (c) rake angle, and (d) tool edge radius.

Fig. 12. Failed elements as microcracks in the shear zone: (a) f¼ 25 μm; (b) f¼ 50 μm; (c) f ¼75 μm; (d) f¼ 100 μm. (Process parameters: V ¼ 3 m/min, γ ¼51, Tool-Up sharp, element size¼ 10 μm.)

Table 4 Effect of feed on contribution of microcrack to specific shear zone energy. (Process parameters: V ¼ 3 m/min, γ¼ 51, Tool-Up sharp.) White marked failed elements as microcracks in thick shear zone

Feed (μm) Shear angle (deg) Cutting force (N) No. of microcracks U sShearZone (N/mm2) U sMicrocrack (N/mm2) % Contribution

25 35.70 10.20 1 502.91 13.80 2.75

50 33.23 17.58 4 962.77 104.08 10.81

One of the parameters that affects the number of microcracks formed in metal cutting using FE model is element size. Due to this limitation of the FEA-based technique, this study quantifies the contribution of microcracks to the specific shear zone energy instead of the number of microcracks in the shear zone. Even though, the number of microcracks has been evaluated as a function of the element size used in FEA model, it is found that their number increases as element size decreases. This is due to the presence of the increased number of elements in the same stress field. Although, the number of microcracks increases, the contribution of microcracks to specific shear zone energy remains almost the same because, the overall volume of shear zone and volume of microcrack remains the same.

4.2. Contribution of microcracks to specific shear zone energy The contribution of the energy associated with the microcrack formation in specific shear zone energy during orthogonal cutting has been evaluated by knowing specific microcrack energy. In the present study, the following approach to quantify the contribution of microcracks to the size effect has been proposed. In FEA model, specific shear zone energy is calculated using the

75 31.53 24.58 6 2030.05 343.28 16.91

100 24.78 30.92 7 2800.49 554.77 19.81

following equation: U sShearZone ¼

Σ IEElementsShearZone V ElementsShearZone

ð12Þ

The contribution of microcracks has been evaluated using specific shear zone energy and specific microcrack energy. The specific microcrack energy is calculated by taking a ratio of sum of energy of all microcracks (i.e., failed elements) to volume of shear zone elements using the following equation: U sMicrocracks ¼

Σ IEmicrocracks V ElementShearZone

ð13Þ

The specific microcracks energies for various parametric conditions and their contribution to the specific shear zone energy are given in Tables 4–7. These tables show a variation in the number of microcracks, shear angle, cutting forces, and contribution of microcracks to specific shear zone energy as a function of cutting parameters. As mentioned earlier, the failed elements in the FEA model are termed as microcracks and they are colored white in the thick shear zone. The present study reports that contribution of microcracks to the specific shear zone energy is in the range of 0–20% under various cutting conditions during orthogonal cutting of AISI 1215.

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D. Parle et al. / International Journal of Machine Tools & Manufacture 80-81 (2014) 18–29

Table 5 Effect of cutting speed on contribution of microcrack to specific shear zone energy. (Process parameters: γ ¼51, Tool-Up sharp, f ¼75 μm.) White marked failed elements as microcracks in thick shear zone

Cutting speed (m/min) Shear angle (deg) Cutting force (N) No. of microcracks U sShearZone (N/mm2) U sMicrocrack (N/mm2) % Contribution

1 30.86 27.11 4 1840.14 185.30 10.07

2 31.03 25.99 5 1953.80 249.89 12.79

3 31.53 24.58 6 2030.05 302.68 14.91

4 32.83 24.07 5 2380.54 269.24 11.31

Table 6 Effect of rake angle on contribution of microcrack to specific shear zone energy. (Process parameters: V ¼3 m/min, Tool-Up sharp, f¼ 75 μm.) White marked failed elements as microcracks in thick shear zone

Rake angle (deg) Shear angle (deg) Cutting force (N) No. of microcracks U sShearZone (N/mm2) U sMicrocrack (N/mm2) % Contribution

5 24.58 28.50 7 1607.27 270.98 16.86

0 28.54 27.08 6 1793.84 269.43 15.02

5 31.53 24.58 6 2030.05 302.68 14.91

10 36.41 21.77 4 2268.14 232.48 10.25

Table 7 Effect of tool edge radius on contribution of microcrack to specific shear zone energy. (Process parameters: V ¼3 m/min, γ ¼ 51, f¼ 75 μm.) White marked failed elements as microcracks in thick shear zone

Tool edge radius (μm) Shear angle (deg) Cutting force (N) No. of microcracks U sShearZone (N/mm2) U sMicrocrack (N/mm2) % Contribution

Up-sharp 31.53 24.58 6 2030.05 302.68 14.91

25 28.49 26.57 7 1810.93 302.60 16.71

Fig. 13a–c shows that the specific cutting energy increases with a decrease in feed in the presence of microcracks. This increasing trend in the specific cutting energy at lower feed is termed as the size effect [29]. In further analysis, the effect of cutting speed, rake angle and tool edge radius is investigated on the specific cutting energy. The specific cutting energy is observed to decrease with an increase in the cutting speed (see Fig. 13a) due to a decrease in cutting forces at higher speeds. A decreasing trend in specific cutting energy is observed with an increase in rake angle (see Fig. 13b). This could be explained by the decrease in the cutting forces due to reduced ploughing at higher rake angles. Similarly, specific cutting energy increases with an increase in tool edge radius as shown in Fig. 13c. This is due to the increase in cutting forces as tool edge radius increases.

5. Microcrack formation during orthogonal cutting of medium carbon steel To demonstrate applicability of the proposed model of microcrack formation discussed in Sections 2–4, to different materials,

75 26.43 28.90 8 1704.34 307.80 18.06

100 24.23 30.45 8 1583.47 310.04 19.58

FE simulations and orthogonal micro-cutting experiments were performed on medium carbon steel (AISI 1045). To identify microcracks in FEA model of AISI 1045, strain-based failure criteria (see Eq. (14)) developed by Wierzbicki and Bai [30] has been used.

εfailure ¼ 0:977e  2:216η

ð14Þ

The FE analysis involves pure Lagrangian approach with adaptive re-meshing using LS-DYNA. Geometry, meshing, boundary conditions and process parameters are as discussed in Section 2.2.1. The cutting tool is made of tungsten carbide and has been modeled as a rigid body. Elasto-plastic behavior of workpiece material has been modeled using Johnson–Cook [20] model. J–C parameters for AISI 1045 were obtained from literature [31]. Table 8 shows overall work material properties used in the FE simulation of orthogonal cutting of AISI 1045. Chip formation uses pure deformation based criteria with adaptive re-meshing during orthogonal cutting in the simulations on AISI 1045. Validation of FEA simulation involves a comparison of cutting forces of FE simulation with the experimental results. A total of 48 experiments were performed with 50% repetitions using

Specific Cutting Energy (N/mm2 )

D. Parle et al. / International Journal of Machine Tools & Manufacture 80-81 (2014) 18–29

27

3000

V = 3 m/min Tool = Up sharp

= 5 deg Tool = Up sharp

2500

V = 3 m/min = 5 deg

2000 1500 1000 500 25

50

75

100

25

Feed (micrometer)

50

75

100

Feed (micrometer)

25

50

75

100

Feed (micrometer)

Fig. 13. Variation of specific cutting energy with (a) cutting speed, (b) rake angle, and (c) tool edge radius.

Table 8 Material properties for workpiece [31]. Properties

Workpiece

Material

AISI 1045

Mechanical properties Density (kg/m3) Young's modulus (MPa) Poisson's ratio

7800 200,000 0.3

Thermal properties Thermal conductivity (W/m 1C) Heat capacity (J/kg 1C) Melting temperature (1C) Thermal expansion co-efficient (m/m 1C)

47.7 432.6 1460 0.000011

Johnson–Cook (J–C) parameters A B 553.10 600.80

C 0.234

m 0.013

therefore the high stresses and strains are induced which results in an increased number of microcracks. Fig. 14d shows increasing trend in the microcracks with an increase in the tool edge radius. Table 9 shows microcracks in the shear zone and their contribution to specific shear zone energy during orthogonal cutting of AISI 1045. The present study reports that contribution of microcracks to the specific shear zone energy (i.e., size effect) in the range of 0– 15% under various cutting conditions during orthogonal cutting of AISI 1045.

6. Summary and conclusions

n 1.00

In this work, failure criterion has been successfully evaluated using the Shaw's hypothesis [13] of microcrack formation. The failure criterion has been modeled to identify, the number, the location and the contribution of microcracks to the specific shear zone energy in the framework of FEA. Some of the main conclusions from this study are as follows:

 A mathematical formulation has been developed to define various parametric conditions (see Table 1) with the experimental setup shown in Fig. 6. Average cutting force is 49.77 N during experiments, whereas it is 47.80 N from FEA simulations when using 75 μm feed and 3 m/min cutting speed with 51 rake sharp tool. Error in FEA simulation and experimental average cutting force is 3.95% for given cutting conditions. Moreover, overall % error for several other cutting conditions does not exceed 10.0%. A quantitative variation in the number of microcracks with the processing parameters is shown in Fig. 14a–d during orthogonal cutting of AISI 1045. Also, for comparison purposes the number of microcrack data generated in the orthogonal cutting of AISI 1215 is presented in Fig. 14. Overall, it is observed that trends in the number of microcracks in the AISI 1045 and AISI 1215 are identical. In all the cases, the number of microcracks in AISI 1045 is lesser than AISI 1215 under similar cutting conditions. This could be because of higher normal stresses in the shear zone of AISI 1045 than that of in the AISI 1215. A steady increase in the number of microcracks from 1 to 7 is observed on increasing feed from 25 mm to 100 mm in AISI 1215 steel, see Fig. 14a. Note that the plastically deformed volume increases with an increase in feed leading to increased number of microcrack formation. The number of microcracks increases from 4 to 6 with an increase in the cutting speed from 1 m/min to 4 m/min, see Fig. 14b. The number of microcracks decreases from 7 to 4 when the rake angle is increased from  51 to 101 (see Fig. 14c). The deformation is severe at negative rake angles and











failure criteria based on Shaw's hypothesis and has been successfully used to identify the microcrack in shear zone during orthogonal cutting. Orthogonal cutting process has been successfully simulated using commercial FEA tool – LS-DYNA. The FE model has been validated using orthogonal micro-cutting experiments for cutting force. The predicted results using FE simulations are in good agreement with the experimental results and overall % error does not exceed 11.50%. A positive intercept of cutting force has also been observed which indicates the presence of fracture component during separation of material in metal cutting, which is also one of the causes of size effect. A quantitative variation of number of microcracks (i.e., failed elements) with processing parameters has been studied. Microcracks increase with an increase in feed and tool edge radius. They decrease with an increase in rake angle, whereas no specific trend is observed with an increase in cutting speed. The contribution of microcracks is evaluated using specific shear zone energy and specific microcrack energy. The contribution of microcracks to the specific shear zone energy is in the range of 0–20% under various cutting conditions for low carbon steel. To demonstrate the applicability of the proposed model of microcrack formation to different materials using FE simulations, orthogonal micro-cutting experiments were performed

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D. Parle et al. / International Journal of Machine Tools & Manufacture 80-81 (2014) 18–29

No. of Microcracks

10

AISI 1215

8

6

6

6

5

6 4

4

4

3

2 1 0

1

0 25

50

8

AISI 1045

7

75 100

Feed (Micrometer)

2

2

1

2

7

5

3

3

3

4

Cutting Speed (m/min)

4

-5

6 6

6

6 4

3

0

2 5

8

7

2 10

3

0

7

4

25

50

75

Rake Angle (Deg.) Tool Edge Radius (Micrometer)

Fig. 14. Microcrack formation with (a) feed, (b) cutting speed, (c) rake angle, and (d) tool edge radius.

Table 9 Contribution of microcracks to specific shear zone energy (AISI 1045). (Process parameters: V¼ 3 m/min, γ ¼51, Tool-Up sharp.) White marked failed elements as microcracks in thick shear zone

Feed (μm) Shear angle (deg) Cutting force (N) No. of microcracks U sShearZone (N/mm2) U sMicrocrack (N/mm2) % Contribution

25 36.76 15.94 0 623.31 0 0

50 34.38 26.69 1 1398.65 30.63 2.19

on medium carbon steel (AISI 1045). It is observed that the contribution of microcracks to the specific shear zone energy is in the range of 0–15% under various cutting conditions in this material.

75 32.25 35.85 3 2283.49 138.84 6.08

100 28.88 47.80 6 3100.67 464.48 14.98

available for carrying out the experimental work required for this research.

Appendix A. Simulation results at higher cutting speeds

Acknowledgment Authors thank Prof. Anil Sahasrabudhe, Director, College of Engineering, Pune (India) for making micromachining facility

Additional simulations were performed at higher cutting speeds of 25 m/min and 50 m/min. The results show that the cutting forces are between 23 and 24 N, at these cutting speeds and the number of microcracks are in the range of 6–7. Other results at these speeds are tabulated in Table A1.

Table A1 Results at higher cutting speeds. (Process parameters: γ¼ 51, Tool-Up sharp, f¼ 75 μm, work material¼ AISI 1215.) White marked failed elements as microcracks in thick shear zone

Cutting speed (m/min) Shear angle (deg) Cutting force (N) No. of microcracks U sShearZone (N/mm2) U sMicrocrack (N/mm2) % Contribution

25 31.84 23.35 7 2195.19 379.98 17.31

50 29.94 23.13 6 2287.86 365.60 15.98

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