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L. ChuzhoySr. Engineering Specialist-R&D

Caterpillar Inc.,Technical Center,Peoria, IL 61525

R. E. DeVorProfessor

S. G. KapoorProfessor

Department of Mechanical and IndustrialEngineering,

University of Illinois,Urbana-Champaign, IL 61801

Machining Simulation of DuctileIron and Its Constituents, Part 2:Numerical Simulationand Experimental Validationof MachiningTo understand the influence of cast iron microstructure on its machinability, a numemodel that simulates machined material on a microstructure scale was developedmicrostructure-level model assembles individual constituents into a composite mabased on microstructural composition, grain size, and distribution. Extensive experitation was performed to determine strain, strain rate, temperature, and load hisdependent material properties. The purpose of this work is to validate the microstruclevel model on machining of ductile iron and two of its constituents: pearlite and ferOrthogonal cutting experiments were conducted of the three materials. The measuremorphology and machining forces were compared with the model predictions, and acorrelation between them was found.@DOI: 10.1115/1.1557295#

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IntroductionThe finite element method has been extensively used to

understanding of material behavior during [email protected]. @1,2##.The method permits computation of deformations, strastresses, strain rates, and temperatures during the process.quantities are extremely difficult to measure or compute anacally. In addition, the finite element method can provide an insiinto a process, since all the results are resolved in both timespace domains.

Existing finite element models have been developed onmacroscopic scale treating a material as homogeneous. Howmany ferrous materials, particularly cast irons, have a highly herogeneous structure. To simulate machining of this class ofterials, a microstructure-level model was developed@3#. Thismodel generates pearlitic and ferritic grains and graphite nodor flakes, and, then, assembles them together to explicitly simumicrostructure of cast irons. An internal state variable mocalled the BCJ model@4# is used to describe the individual behaior of pearlite, ferrite, and graphite. The material model captuthe behavioral dependency of each constituent on strain, srate, temperature, direction of loading, and amount of damag

Part 1 of this paper dealt with material model characterizatand validation. Validation of the material model was isolated frovalidation of the machining simulation to test the accuracymaterial model without the complexities of machining. The marial parameters of the individual constituents were determineaccount for effects of two important phenomena associatedmachining: permanent material softening upon reverse loadand material damage. Uniaxial reverse loading experimentssimulation were performed to determine the material paramefor the effect of permanent material softening upon reverse loing. The characterization was conducted on pearlite and ferwhile the validation is done using ductile iron. The damagerameters were determined from pearlitic, ferritic, and ductile irnotched specimens. A single notch radius was chosen for chaterization, and three notch radii are chosen for validation.

Part 2 of this paper deals with machining validation of t

Contributed by the Manufacturing Engineering Division for publication in tJOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript receivedJune 2001; revised October 2002. Associate Editor: Y. Shin.

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microstructure-level model. Both experimental work and simution are done using orthogonal machining to focus on the rolematerial microstructure. Photomicrographs of the collected chare examined to quantify chip dimensions. The machining forare measured during the tests. Predicted chip morphologycutting forces undergo detailed examination. The experimedata and simulation results are compared and discussed.

Numerical SimulationThree microstructures were used for the simulated workpie

pearlite, ferrite, and ductile iron. Four simulations were performon each material using the test matrix shown in Table 1. The deof cut and edge radius were chosen as variables to validatemodel under changing process parameters. Two levels ofdepth of cut were tested: 75mm and 125mm. Three levels of theedge radius were used: 25mm, 50mm, and 75mm. The selectionof the 50mm edge radius was motivated by an interest to examinfluence of the edge radius to the depth of cut ratio on modperformance. Machining with the 50mm edge radius was selectefor case 1 to approximate the edge radius to the depth of cut rof case 4. The selected values of the cutting depth provide grange for microstructure-level model validation, since the depthcut is of the same order of magnitude as material grains. In ation, the low range of the depth of cut can be used to evalumodel’s applicability to micro/meso-level machining.

Numerical Model. The microstructure-level model used ithis study explicitly models material microstructure during mchining simulation. A finite element model is generated by defiing grain boundaries and, then, enmeshing grains using a comcial pre-processor@5#. The material behavior of each constituentcaptured with an internal state variable model called the Bmodel @6#. Extensive experimentation was conducted to defimaterial characterization parameters for the BCJ model. Themodel is integrated with a processor of a commercial finite ement code@7#. The finite element model is periodically remeshand rezoned to avoid excessive distortion elements and remdamaged elements. A detailed model description and resultindividual constituent characterization are provided in@3# and inPart 1 of this paper.

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A plane strain ~two-dimensional! approximation was usedthroughout this study. The workpiece was modeled as a rectalar block consisting of a single microstructure meshed with bilear quadrilateral elements. The bottom nodes were constraboth vertically and horizontally, while the nodes at the left bounary were constrained only horizontally. The cutting tool wassumed to be perfectly rigid. The tool was constrained againsttical displacement and rotation. Loading was accomplishedspecifying incremental tool displacement in the horizontal dirtion and time to perform this step. To avoid the effects of moconstraints, the cut was terminated prior to reaching theboundary. The length of the cut was 720mm and its duration was0.0009 second corresponding to the cutting velocity of 48 m/m

The height and length of the workpiece were determinednumerical experimentation using changes in machining forceschip geometry as the convergence criteria. To improve comptional efficiency, the workpiece was divided into two layers. Tupper layer was meshed with the average element size of 10 tmm, while the bottom layer had the average element size betw40 and 60mm. Mesh fidelity was also tested numerically bchanging mesh size and using changes in machining forceschip geometry as the convergence criteria. The workpieceremeshed and rezoned ninety times to maintain a reasonablement shape and aspect ratio. It was decided not to use adameshing around the tool tip for two reasons. First, although adtive meshing can effectively reduce run time, local mesh refiment may cause preferential displacement since a fine mesgenerally less stiff than coarse mesh@8#. Second, it is impracticato use adaptive meshing for general microstructure-level mosince it already has very fine mesh required for enmesh grain

The ductile iron workpiece was modeled using two sizesrectangular blocks with dimensions of 300mm by 700mm for 75mm cut, and 400mm by 900 mm for the 125mm cut. It wasacceptable to use a smaller workpiece model for ductile iron sthis material is less ductile than either ferrite or pearlite and, thefore, has a smaller region affected by machining. The minimsize of the workpiece was numerically tested based on thevergence of the cutting force. The workpiece size was doubuntil a change in the computed cutting force was less thanThe workpiece microstructure for ductile iron is shown in Fig.The dark cylinders representing graphite nodules are surrounby ferrite shown with light colored hexagons. Pearlitic matrixshown with dark colored hexagons. The model contained 1graphite, 40% ferrite, and 50% pearlite measured by volumediscussed in@3#. The distribution and size of graphite nodulewere determined randomly using the Monte Carlo method. Tgraphite nodule diameter was between 30 and 50mm and size offerritic and pearlitic grains is 80mm.

The analysis assumes adiabatic heating with the temperaincreaseDu governed by the following equation:

Fig. 1 Simulated workpiece microstructure for ductile iron

Table 1 Process parameters

Test Case # Depth of Cut~mm! Edge Radius~mm!

1 75 502 75 753 125 254 125 75

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Transient thermal analysis was conducted to study convecand conductive heat removal during machining. It was establisthat the amount of heat removed during 0.0009 second of thewas insignificant. Therefore, adiabatic heating provides a reaable approximation of the process.

Fig. 2 Machining forces from cutting simulation of „a… pearlite,„b… ferrite, „c… ductile iron

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Sticking is assumed between the tool and the workpiece. Tassumption is justified since the uncoated inserts were usedthe cuts were shallow. Sticking is modeled by setting the relattangential velocity between the contact surfaces of the tool andworkpiece to zero. Full contact between the tool and the wopiece leads to increased plasticity mimicking a boundary~‘fluid’ !layer observed in literature@10#.The material damage ratef was computed as follows:

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wherep is the hydrostatic pressure,seff is the effective stress, andn is the parameter determined experimentally on individual cstituent basis as described in Part 1.

A significant amount of damage generally occurs during mchining of ductile iron leading to formation of semi-continuousdiscontinuous chip@11#. To prevent rigid body motion associatewith loose elements, the program continuously removes portiof the ‘‘damaged’’ grains from the workpiece. This techniquesimilar to element erosion used by several researchers~e.g.@12#!.

Simulation Results. Since the objective of this work was tocorrelate numerical model results with experimental data,simulation results presented below focused on chip type andometry, and machining forces. Although temperature, strainstress distributions were computed, quantitative experimemeasurements were not available for comparison purpose.results are divided into two parts. First, the simulation resurelated to the machining forces are discussed. Then, the simularesults related to chip formation are presented.

Machining Forces

Pearlite. The computed cutting and thrust forces for case 1the pearlitic specimen are shown in Fig. 2~a!. It was observed thatthe cutting force clearly exhibits five cycles for the 75mm cutsand four cycles for the 125mm cuts. These cycles correspondformation of shear localization zone. The cutting force at the peof the first cycle is always smaller than at the peaks of the folloing cycles. This relationship is due to unconstrained behaviothe first chip segment in the direction of chip flow. It was al

Fig. 3 Influence of chip formation on cutting and thrust forcesfor machining of pearlite „case 1 …

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observed that the cutting force stabilizes after the first two cycThe thrust force displays a less pronounced periodicity and stlizes after the second shear localization cycle.

Fluctuations of the cutting and thrust forces are closely linkto chip formation~see Fig. 3!. The cycle begins just after a serration initiates~see inset~a!!. At this point, the width of the shealocalization zone is approximately one half of its final value. Tshear angle is the smallest during the cycle~the shear angle isdefined by a line connecting the tool tip with a point at the frsurface where the chip forms!. The region around the tool tip is aelevated temperature and, therefore softer than the surrounmaterial. As the tool advances, the shear localization zone widand slides upwards leading to a rise in the thrust force. Initiathe cutting force is reduced due to the growth on the shear loization zone~see inset~b!!. However, the upward movement othe shear localization zone causes the tool to plough throstronger material leading to increase in the cutting force. Theting force reaches its peak when the chip is at its lowest thickn~see inset~c!!. At this point, the ratio between the cutting anthrust forces is the largest, which can be explained by the higvalue of the shear angle. Next, the material around the toolstarts to soften leading to formation of the shear localization zand a sharp drop in the cutting and thrust forces~see inset~d!!. Asanother chip serration is formed, the process repeats itself.

Ferrite. Figure 2~b! provides the simulated cutting and thruforces for machining of ferrite~case 1!. Complete force stabiliza-tion takes up to 400mm. It was observed that for the 125mmdepth of cut the thrust force initially rises to a value higher ththe one achieved at equilibrium. This indicates that material sens during cutting. The cutting forces show a moderate amounfluctuation, while the thrust forces display little fluctuation. Thcan be explained by linking machining forces to chip formatioThe ferrite chip has wide primary and secondary shear zones~seeFig. 5~e!–~h!! with a gradual transition into less strained~cooler!parts of the chip. This indicated that the machining forces requto machine ferrite do not have large fluctuations. In addition,area around the tool tip remains at nearly the same temperaduring machining in the stabilized region essentially acting asenergy absorber for the tool.

Ductile Iron. The cutting and thrust forces for the simulateductile iron microstructure are shown in Fig. 2~c!. It was observedthat the forces display a strong dependence on the depth ofThe peak values of the cutting force range between 400 N andN for the 75mm cuts and between 600 and 680 N for the 125mmcuts. The peak values of the thrust force vary between 250 N300 N for the 75mm cuts and between 400 and 450 N for the 1mm cuts.

The cutting mechanism of ductile iron combines shear localtion and material damage. Because graphite has much lostrength than ferrite and pearlite, a shear localization zone usupasses through graphite nodules. In addition, graphite noduleas initiation sites for fracture, eventually creating the segmenchip. Therefore, the machining forces are strongly influencedmaterial composition and the depth of cut. Since the chip is smented, the tool edge radius does not significantly influencemachining forces.

Chip Morphology

Pearlite. The machining simulation of pearlite computed fomation of a serrated chip. The chip formation and temperadistribution of pearlite are shown in Fig. 4. As the tool initiatmaterial movement, a localization zone occurs near the too~Fig. 4~a!! followed by plastic deformation in the primary ansecondary shear zones~Fig. 4~b!!. Since the temperature increasis proportional to plastic deformation and material strength,temperature rapidly rises in the shear zones which, in turn,duces material strength there. The high temperature in the secary shear zone creates a thin boundary layer that allows



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Fig. 5 Predicted chip morphology for machining of „a…pearlite-case 1, „b… pearlite-case 2, „c… pearlite-case 3, „d…pearlite-case 4, „e… ferrite case 1, „f … ferrite-case 2, „g… ferrite-case 3, „h… ferrite-case 4

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movement along the tool face zones. The temperature rise athe primary shear zone permits the upper portion of the chipslide along the primary shear zone creating a serrated chip~Fig.4~c!!. The high temperature band initiates near the tool tip~Fig.4~d!! and propagates towards the free surface~Figs. 4~e!–~f !!. Asthe material slides, most of the deformation occurs in the matewhich is hotter and, therefore, weaker. Thus, the rate of tempture increase significantly drops~Fig. 4~g!!. The sliding continuesuntil the tool tip enters a cooler and, therefore, stronger materegion ~Fig. 4~h!!. At this point, the temperature increases agaand the process repeats itself~Fig. 4~i!! until the cut is complete~Fig. 4~k!!. The simulated cutting mechanism was similar todescription provided by Komanduri et al.@13# based on their ex-perimental observations using high-speed photography.

All four cases of machining simulation of pearlite showed simlar chip formation and temperature distribution patterns~see Fig.5~a!–~d!!. When simulation was performed for case 1 that hadmm depth of cut with 50mm tool edge radius, five peaks~cycles!in the serrated chip were predicted for the 720mm long cut~seeFig. 5~a!!. The chip geometry stabilized after the second cycThe smallest and largest chip cross-sections~see Fig. 6! were 95mm and 180mm, respectively. The distance between the peaksthe last four cycles was around 110mm. The primary shear zonecontained large temperature gradient that indicated ‘‘slidinplanes of chip segments. Since the segments were able to mrelative to each other, chip curvature was small. Althoughworkpiece showed only insignificant surface waviness, the plastrain plots indicated periodic changes near the surface.

Ferrite. The simulated ferritic specimen behaved differenthan the pearlitic specimen. Although ferrite also generated atemperature in the primary shear zone~see Fig. 5~e!–~h!!, thetemperature increase and material characteristics preventednounced formation of shear localization. As the tool travthrough the workpiece, broad temperature bands form in the cThe increased temperature causes a small amount of slidinoccur putting a wave-like appearance on the chip surface oppto the tool. The surface deformation increases as the chip cmaking the wave height equal to 10–15% of the total chip thiness.

The ferrite chip thickness for case 1 was approximately 190mm~Fig. 5~e!!. Six cycles occurred during the simulated cut with tprocess stabilizing after the third cycle. The interior temperatof the chip varied less than the temperature of the pearlitic cBecause of the decreased temperature gradient in ferrite, itsdisplayed a moderate amount of curvature. The machined wpiece surface appeared to be reasonably straight, althoughfluctuations in temperature and equivalent plastic strain were snear the surface.

Ductile Iron. The chip formation mechanism for ductile irois more complicated than those described above. A sequencsimulated material is shown in Fig. 7 and follows descriptiprovided in @3#. As the tool plows through the workpiece, largdeformations occur in graphite and ferrite. The damage accu

Fig. 6 Pearlite chip dimensions for case 1 machining param-eters

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lates near the tool tip leading to a segmented~fractured! chip. Inaddition, shear localization occurs around the primary shear zThe shear localization placement often coincides with locationgraphite in that region~see Fig. 7~a!, ~c!, and~d!!. Graphite nod-ules in the shear localization region experience a significamount of elongation in the direction of chip flow. The graphnodules at the free surface were extruded from the material.chip is removed to prevent computational difficulties associawith rigid body motion and complicated sliding associated wloose material. The tool travels almost freely through the wopiece until it encounters the next cycle.

For case 1 the chip thickness was approximately 90mm, whichwas slightly higher than the depth of cut. The segment lengththe chip averaged to 90mm. This leads to a conclusion that if thchip segments remain attached, the chip has tight curl. Sinceriodic fracture occurred in the ductile iron chip, its temperatuwas relatively low ranging between 100°C and 250°C.

Orthogonal Machining Experiments

Material and Experimental Procedure. The machining ex-periments were performed on workpiece materials with threetinct microstructures. One material was pearlitic-ferritic ductiron, while the other two were single structure steels with fupearlitic and fully ferritic microstructures. The single structusteels were chosen to mimic behavior of two constituents of dtile iron: pearlite and ferrite. The heats of single structure stewere custom made. They contained the same alloying elemexcept for the amount of carbon as ductile iron. Each heatvacuum-induction-melted and poured into a 50 lb ingot mold. Tingots were reheated to 2250 F~1232°C! for ferritic compositionor to 2050 F~1121°C! for pearlitic composition. The ingots werthen rolled into 1.7 inch~43.18 mm! square bars. All bars were aicooled after rolling. One of the steels had fully pearlitic micr

Fig. 7 Simulated deformed grains of ductile iron at cutting dis-tance of „a… 0.06 mm, „b… 0.17 mm, „c… 0.28 mm, „d… 0.40 mm



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Table 2 Average „amplitude … machining forces

Cutting Force, N Thrust Force, NMaterial Case 1 Case 2 Case 3 Case 4 Case 1 Case 2 Case 3 C

Pearlite 590 620 850 1050 480 600 650 850~Measured! ~200! ~170! ~280! ~350! ~120! ~110! ~70! ~200!

Pearlite 550 570 780 960 500 610 500 770~Predicted! ~200! ~190! ~300! ~320! ~100! ~120! ~50! ~150!

Ferrite 520 540 800 850 480 510 700 650~Measured! ~20! ~30! ~40! ~70! ~20! ~30! ~40! ~60!

Ferrite 500 510 740 850 390 510 410 640~Predicted! ~30! ~20! ~50! ~100! ~15! ~20! ~20! ~50!Ductile Iron 370 380 600 610 270 300 420 480~Measured! ~80! ~90! ~200! ~190! ~60! ~100! ~150! ~250!Ductile Iron 350 360 560 580 200 270 380 370~Predicted! ~300! ~200! ~320! ~350! ~210! ~200! ~300! ~200!

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structure, while the other steel was fully ferritic. Their chemiccompositions and details of manufacturing methods for the expmental heats can be found in@3#. It should be noted that all material characterization and machining experiments describeboth parts of this work were performed on the same material

Upon test completion, material microstructures were examiat several locations and were found to be consistent. The peasteel had completely pearlitic microstructure with average grsize of 20 microns. The ferritic steel had pure ferritic microstruture with average grain size of 100 microns. Ductile iron wcomposed of 50% of pearlite, 40% ferrite, and 10% graphite. Tgraphite nodule diameter ranged between 20 and 60 microns

The workpiece had 41.3 mm square cross-section and 15.9height with two ribs on top. This specimen design was develoto perform orthogonal cutting on a flat workpiece enabling costant machining parameters to be controlled. The machiningperformed on a Mori Seiki ZL-250 twin turret CNC lathe with thworkpiece mounted on one turret and the tool mounted indynamometer on the opposite turret. Both turrets moved towaeach other to obtain cutting velocity of 48 m/min. The workpiewas rigidly clamped on the four sides perpendicular to the cutplane and was supported on the backside. The width of cutequal to the width of each rib, which was 3.175 mm.

The machining was done with Kennametal grade K3TPG432 inserts. These are uncoated inserts commonly usecast irons. The tool had a negative 7 deg rake angle and a pos18 deg clearance angle. The insert edges had radii of 25, 5075 mm. After an edge was used for two cuts, an insert was eirotated or replaced.

The cutting and thrust forces were measured with a Model 9Kistler turning dynamometer. Data was recorded at 60,000sampling rate. The lateral force was also monitored to assuredimensional nature of machining. In all the experiments the latforce was two orders of magnitude smaller than the cuttingthrust forces.

The test matrix for each material was the same as the simtion matrix that is shown in Table 1. The machined surfaces ofthree materials looked dramatically different. The pearlitic spemen produced a rather clean cut that looked like a polishedface with periodically located ridges in the direction perpendicuto the cut. The pearlitic specimen had very little burr on the siand the end. The ferritic specimen exhibited ductile behaviorating a smeared surface with side flow and burrs at the end ofThe ductile iron clearly displayed brittle behavior. The workpiesurface was extremely rough showing surface damage visiblea naked eye. The amount of surface damage varied in the dtions parallel and perpendicular to the cut.

Prior to actual testing, reference cuts were performed to asthat the actual cutting depths were correct. Replicates of eachrun were conducted to assure its repeatability. Chips werelyzed from the experiments with 75mm depth-of-cut and the 50



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Experimental Results and Comparison With Simulation.Following the structure of the previous section, the discussiodivided into two parts. First, the measured machining forcesreviewed and compared with the computed forces. Then, the msured chip morphology is compared with the simulated chips.

Machining Forces. The measured cutting and thrust forcwere examined and compared with the simulated forces. Theperimental forces were averaged over the stabilized regions oentire cut to compare their magnitudes and trends with the cputed forces~see Table 2!. Measured force fluctuations were stuied to compare local behavior of experimental and predicforces. Figure 8 show samples measured machining forces plousing the same scale as the scale used for the simulation plo

Pearlite. The measured cutting forces increased by 50–6with the increase in the cutting depth from 75 to 125mm ~seeTable 2!. The edge radius increase clearly elevated both theting and thrust forces. The experimental thrust forces were alwlower than the cutting forces. The ratio between the thrust foand the cutting force was proportional to the edge radius todepth of cut ratio. The fluctuation of the measured forces had wdefined large cycles as shown in Fig. 8~a!.

The average values of the simulated forces were within 15%the experimental forces. The simulated and experimental foshowed the same dependence on the edge radius, the depth oand the ratio of the edge radius to the depth of cut. Both simulaand measured cutting forces had fluctuation amplitude betw200 and 300 N. The thrust forces also had similar fluctuatamplitudes. For machining with the small radius and large deof cut ~case 3!, both the predicted and measured thrust forcshowed significantly less fluctuation than the thrust forces forother three cases. This phenomenon is explained in the nexttion during the examination of chip morphology.

Ferrite. The measured cutting and thrust forces for ferrifirst, increased and, then, stabilized after the first 10 millimetercutting. Increasing the cutting depth from 75 to 125mm led toabout 25% increase in the cutting forces. The edge radius incrdid not noticeably change the cutting and thrust forces. Fofluctuation was less pronounced compared to pearlite~see Fig.8~b!!. The force cycles were not well defined. It is interestingnotice that the cutting and thrust forces are within 10–15% forfour cases.

For machining of ferrite with the largest edge radius tool, tcutting and thrust forces are within 10% for simulation and eperiments. The only noticeable difference between computedmeasured forces occurred in the thrust force prediction for cut

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125 mm with 25 mm edge radius~case 3!. One possible explanation for this discrepancy can be the formation of a built-up edwhich occasionally occurs when a soft material is machined wan uncoated sharp tool. The amount of local force fluctuationvery close for the simulated and experimental forces.

It should be noticed that the forces for the 75mm cutting depthdid not significantly vary between ferrite and pearlite. Althouthe low strain rate yield strength of ferrite is about three timlower than the strength of pearlite@3#, ferrite exhibits more workhardening than pearlite. In addition, pearlite is more sensitivepermanent softening upon reverse loading and elevated temture than the ferrite~see Part 1 of this paper!. Ferrite generated

Fig. 8 Samples of measured machining forces from cutting ofwith parameters of „a… pearlite, „b… ferrite, „c… ductile iron

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less heat and was less sensitive to shear localization. The mcorrectly captured and explained the described phenomena.

Ductile Iron. Unlike the single constituent materials, the dutile iron forces had local waviness that probably correspondemicro-rupture discussed above. The cutting force increased byproximately 50% when the cutting depth was changed frommm to 125mm. The forces also increased when the inserts wlarger edge radii were used. Although the ratio between the thforce and the cutting force was proportional to the edge radiuthe depth of cut ratio, it was not as pronounced as in the caspearlite. Force fluctuation was between 50 and 300 N with lavariability in its duration.

The predicted forces showed the same trends as the meaforces ~see Figs. 2~c! and 8~c!!. However, the average values othe forces were below the measured values. This reflects tdimensional nature of the model, which approximates grainsnodules as extruded volume. Therefore, when a grain is damait simultaneously occurs throughout the width of the workpieleading to a sharp force drop. During the experiments, the matefracture occurred more gradually reducing the force drop. Tpeaks of the cutting and thrust forces were in a good agreemwith the experimental values~see Fig. 8~c!!.

Additional Observations. In general, the computed magntudes of the average forces and their fluctuations agreed wellthe experimental data~see Table 2!. To quantitatively compare thelength of force cycles, the Fast Fourier Transform~FFT! analysiswas performed on the simulated and experimental cutting forfor case 1. The FFT analysis of the measured cutting forcepearlite showed a large peak near 0.45 mm/cycle~1,800 Hz! andsmaller peaks around 0.2 mm/cycle. The computed cycle lenwas 0.17 mm. The analyses of the experimental data for feand ductile iron displayed large spread of the cycle length thatdue to combining cycles of variable amplitudes. The cycle lenof the simulated cutting force was in the lower portion of texperimentally measured range.

Chip Morphology. The chips of the three specimens weexamined after machining with 75mm depth of cut using a toowith the 50mm edge radius~case 1!. A stereo microscope wasused for this purpose. The comparison of the simulated and msured chip morphology is summarized in Table 3.

Pearlite. The pearlite chip was continuous and long. Its thicness was nonuniform with a serrated profile~see Fig. 9~a!!. Thethinnest chip section was 80mm, while the largest section wa180 mm. The distance between two large neighboring peaksapproximately 220mm. It should be noted that two to four smallepeaks occurred between each pair of large peaks that was e

Table 3 Comparison of predicted chip geometry with mea-sured data for case 1

MaterialLargest Chip

Thickness~mm!Smallest Chip

Thickness~mm!

Distance between ChipSerrations or Segments

~mm!

PearlitePredicted

180 95 110

PearliteMeasured

180 80 220

FerriteMeasured

190 160 30

FerritePredicted

210 150 20–60

DuctileIronPredicted

90 90 80–90

DuctileIronMeasured

100 85 70–200



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ined. The structure of the chip was pearlitic indicating that ttemperature was below the austenitizing temperature.

During cutting simulation of pearlite, the model predicted fomation of the serrated chip of similar geometry to the geometrythe actual chip~recall Fig. 5~a!!. The thickness of the highest anlowest chip sections in the simulated chip were within 10% of tmeasured chip. The longitudinal distance between individualrations in the computed chip was shorter than the measured vaThis discrepancy could be explained by examining a photomicgraph of the actual pearlitic chip~see Fig. 9~a!!. The actual chipcontained one to two small serrations that reside between epair of large serrations. This phenomenon was due to formatiosmall shear localization zones between large cycles. The appance of the small peaks indicated that the material attempte

Fig. 9 Photomicrographs of machined chips of „a… pearlite, „b…ferrite, „c… ductile iron, „d… ductile iron-enlargement of „c…



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form a cycle, but the outside constraints prevented it. The difence in serration frequency disappears if the small cyclestaken into account.

The local shape and amount of fluctuation in the simulatedmeasured cutting forces showed strong links to chip formatiThe cutting force for pearlite had large wave-like fluctuations~seeFig. 2~a! and Fig. 8~a!!, which corresponded to formation of larguniformly spaced serrations on the pearlite chip~see Fig. 9~a!!.Cutting with the 25mm edge radius tool produced the smalleserration depth and the largest shear angle~see Fig. 5~e!! reducingforce fluctuations and increasing the ratio between the cuttingthrust forces.

Ferrite. The ferrite chip was continuous and long as shownFig. 9~b!. The chip surface had wavy appearance. The chip thness varied between 150 and 210 microns for the 75mm cut withthe 50mm edge radius~test case 1!. The ferrite chip had slightlytighter curl than the pearlite chip.

The simulated ferritic chip thickness was around 190mm with15% periodic fluctuation~recall Fig. 5~e!!, while the actual chipthickness ranged between 150mm and 210mm. This variation islikely to be due to the influence of surface discontinuities in tback of the chip typical for relatively soft materials@10#. Bothsimulated and experimental chips had wavy appearance withlatter having significant amount of variation between its cyc~see Fig. 9~b!!. This waviness was quantified by measuring tdistance between the chip peaks from the photomicrographs oferrite chip~e.g. Fig. 9~b!!. The distance between the peaks of tsimulated chip was within the range of the experimental measments.

Similar to pearlite, the cutting force for ferrite reflected the chshape. The cutting force had small ripples~see Fig. 2~b! Fig. 8~b!for case 1! which correlated to a wave on the ferrite chip~seeFigs. 5~e! and 9~b!!. Cutting force fluctuation for ferrite wassmaller than pearlite cutting force fluctuation directly correspoing to the difference between the chip shape of ferrite and pear

Ductile Iron. The ductile iron produced short semi-continuochips with a tight curl~see Fig. 9~c!!. The chip thickness wasaround 100mm. It appeared to consist of a series of 40–1micron long sections, which were loosely attached to each otThe graphite nodules were elongated in the direction of chip~seeFig. 9~d!!.

The simulation of ductile iron predicted formation of semented chip with thickness similar to the measured chip thiness. The simulation predicted elongation of graphite nodulessurrounding ferritic grains in the direction of the chip flow, whiccorrelated with the experimental observations~recall Fig. 7!. Themeasurements showed large variation in the chip segment lenThis variation can be attributed to random size and distributiongraphite nodules that vary in the directions perpendicular andallel to the cut~see Fig. 9~c!!. Since the model does not accoufor grain distribution in the plane parallel to the plane of cut, tmodel predicts the chip segment length in the lower range ofexperimental measurements.

The segmented ductile iron chip produced the cutting fowith fluctuation larger than force fluctuation of either constitue~see Figs. 2~c! and 8~c!!. The cutting force had almost triangulashape reflecting formation of the segmented chip.

Additional Observations. In summary, the model producegood results for prediction of chip morphology for pearlite, ferriand ductile iron. It is significant that the tested and simulamaterials formed three different types of chip and had threeferent modes of chip-surface separation. As it was shown in Paof this paper, the model ability to predict chip morphologyinfluenced by modeling and calibration of permanent matesoftening upon reverse loading. The chip-surface separationsimulated with the damage model described in Part 1. The damparameters used in the model differentiated between ductilehavior of ferrite and brittle behavior of pearlite and ductile iron

MAY 2003, Vol. 125 Õ 199


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Additional CommentsThe simulation results provide insight into behavior of the mo

eled materials during machining. The simulation model permitcorrelation of the force variation to the chip shape. The cuttforce reached its highest value when the chip formed its peakthe cutting force dropped, the chip thickness also decreased reing the lowest or separation point simultaneously with the cuttforce. The cutting force was always in-phase with the chip thiness essentially tracing chip shape. This phenomenon wasobserved experimentally by Komanduri et al.@13# who used vari-ous materials to study chip formation. Komanduri and coworksynchronized their force recorder with the high-speed camerato take chip pictures. They observed the same timing betweencutting force and chip formation as the timing described abov

It is appropriate to state here that the microstructure-lemodel validated in this work provides a method to assemble invidual constituents into a composite material. The value of tapproach can be shown by examining the cutting forces for casThe values of the cutting force for ferrite and pearlite were ab600 N. If the rule of mixture is used and the strength of graphis totally ignored, the cutting force for ductile iron should be 5N. However, both the microstructure-level model and the expmental data showed this force to be 400 N demonstrating tharule of mixture is not applicable here.

Although the main objective of this work is to validate thmachining model, it is useful to use the results of this simulatto compare information obtained from a single constituent~homo-geneous! model and a multiple constituent~microstructure-level!model. Figure 10 displays equivalent stress in ferrite and duciron. If the material is approximated as homogeneous, the stdistribution ~as well as any other variable! is continuous. In con-trast, the plot from the microstructure-level model shows thatstress is dramatically different in individual constituents. Pearcarries the majority of the stress, reducing load on ferrite agraphite. Since ferrite has lower strength than pearlite, peargrains locally deform ferritic grains. It is also important to obserthat material flow in the two models is quite different. The sing

Fig. 10 Computed equivalent stress for case 3 at tÄ0.00012 s with „a… ferritic workpiece, „b… ductile iron work-piece

200 Õ Vol. 125, MAY 2003


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structure steel displays uniform material movement, whileductile iron shows dramatically different displacements in neigboring grains. In summary, the microstructure-level model pvides information which is difficult, if possible, to obtain fromhomogeneous model.

The model has another valuable advantage over experimeThe model permits complete isolation of the microstructuresponse during machining. Thus, a study can be conducted exining various microstructures completely independent fromresponse of the machine and tool. If a researcher desires toinclude the system in the study, it may be accomplished by cpling the microstructure-level model with a mechanistic modsimilar to the one described in@14#.

ConclusionsThis effort applied the microstructure-level model to orthogon

cutting of ductile iron and two of its constituents: pearlite aferrite. The experiments were conducted to validate simulatresults. The simulation results generally correlated well withexperimental data for both individual constituents and duciron. The following was observed:

1. The model correctly simulated material behavior and cformation mechanisms for all three materials. The simulation aexperiments showed shear localization for pearlite, ductile flfor ferrite, and chip segmentation for ductile iron.

2. The simulated chip geometry correlated well with the eperimental measurements for all three materials. Small discrecies between the model and the experiments can be explainematerial imperfections that act as stress risers.

3. The predicted magnitudes of the cutting and thrust forwere in agreement with the experimental data. Discrepancielocal cycle duration are attributed to the dynamic response oftool and machine unaccounted by the model.

4. The microstructure level model was successfully validatThe model can be used to study influence of microstructuremachinability of cast irons. The model can simulate microstrtures prior to producing materials allowing their optimization fmachinability.

AcknowledgmentsThe authors gratefully acknowledge the support of Caterpi

Inc. through Management Review Board funding. The authwould also like to acknowledge Mr. Michael Vogler for performing machining experiments. Leo Chuzhoy would like to thankcolleagues at Caterpillar for helpful discussions.

References@1# Strenkowski, J. S., and Caroll, J. T., 1985, ‘‘A Finite Element Model of O

thogonal Metal Cutting,’’ ASME J. Eng. Ind.,107, pp. 349–354.@2# Iwata, K., Osakada, K., and Terasaka, Y., 1984, ‘‘Process Modeling of

thogonal Cutting by the Rigid-Plastic Finite Element Method,’’ ASME J. EnMater. Technol.,106, pp. 132–138.

@3# Chuzhoy, L., DeVor, R. E., Kapoor, S. G., and Bammann, D. J., 20‘‘Microstructure-level Modeling of Ductile Iron Machining,’’ ASME J. Manuf.Sci. Eng.,124, p. 162.

@4# Bammann, D. J., and Johnson, G. C., 1987, ‘‘On the Kinematics of FinDeformation Plasticity,’’ Acta Mech.,70, pp. 1–13.

@5# SAS IP, Inc., 1998,ANSYS Modeling and Meshing Guide, 3rd Edition.@6# Bammann, D. J., Chiesa, M. L., and Johnson, G. C., 1996, ‘‘Modeling La

Deformation and Failure in Manufacturing Processes,’’Theoretical and Ap-plied Mechanics, pp. 359–376, Tatsumi, Wanabe, Kambe, eds.

@7# Hibbitt, Karlson, and Sorensen, 1998,ABAQUS User’s and Theory Manuals,Version 5.8.

@8# Cook, R. D., Malkus, D. S., and Plesha, M. E., 1989,Concepts and Applica-tions of Finite Element Analysis, 3rd Edition, John Wiley & Sons, pp. 558–561.

@9# Farren, W. S., and Taylor, G. I., 1925, ‘‘The Heat Developed During PlasExtrusion of Metals,’’ Proc. R. Soc. London, Ser. A,107, pp. 422–451.



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@10# Shaw, M. C., 1984,Metal Cutting Principles, Bookcraft Ltd.@11# Cohen, P. H., Voigt, R. C., and Marwanga, R. O., 2000, ‘‘Influence of Grap

Morphology and Matrix Structure on Chip Formation during MachiningDuctile Iron,’’ AFS Casting Congress, Pittsburgh, PA.

@12# Ceretti, E., Fallbohmer, Wu, W. T., and Altan, T., 1996, ‘‘Application of 2FEM to Chip Formation in Orthogonal Cutting,’’ J. Mater. Process. Techn59, pp. 169–180.



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l.,

@13# Komanduri, R., Schroeder, T., Hazra, J., von Turkovich, B. F., and Flom,G., 1982, ‘‘On the Catastrophic Shear Instability in High Speed Machiningan AISI 4340 Steel,’’ ASME J. Eng. Ind.,104, pp. 121–131.

@14# Fu, H. J., DeVor, R. E., and Kapoor, S. G., 1984, ‘‘A Mechanistic Model fPrediction of the Force System in Face Milling Operations,’’ ASME J. EnInd., 106, pp. 81–88.

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