advances in numerical modeling of manufacturing … · 2012-07-26 · 347 rajiv shivpuri :...

Trans. Indian Inst. Met.

Vol.57, No. 4, August 2004, pp. 345-366TP 1899

1. INTRODUCTION

Numerical modeling is increasingly being used in thedesign and optimization of manufacturing processesfor the higher quality of the product and improvedproduction yields. Advances in numerical modelingof material behavior, efficient computationalalgorithms, better representation of mechanical andthermal interfaces, and advances in computer hardwareand storage devices have enabled complex softwareto be used for process design and optimization.Several case histories are included in this paper todemonstrate the application of numerical models toproblems relevant to the industrial members of theManufacturing Research Group at the Ohio StateUniversity. Selected case histories are from the steelmills, the forging industry, the die casting industryand the machine shops. Many of these case historiesare applications of numerical models together withheuristic or domain knowledge to improve process

and die designs, and to reduce defects duringproduction. These tools and approaches are necessaryto produce high quality products, and to engineer theproduction systems for high productivity and quickresponse to customer needs.

2. HOT DEFORMATION WITHMICROSTRUCTURE EVOLUTION

2.1 Hot Rolling of Bars: Application in Steel Mills

Recent emphasis on manufacturing rolled products toproperty specifications has resulted in researcherstrying to use thermomechanical history to modelmicrostructural evolution during the rolling process.A typical material conversion process in rolling millsconsists of strand casting, hot rolling of the strandsinto rolled rods, and shearing of rods into billets thatare converted to discrete parts in the forging process,Fig. 1. Often the forgeability of the rolled rod

ADVANCES IN NUMERICAL MODELING OFMANUFACTURING PROCESSES: APPLICATION TO

STEEL, AEROSPACE AND AUTOMOTIVEINDUSTRIES

Rajiv ShivpuriProfessor and Director, Manufacturing Research Group

The Ohio State University, Columbus, Ohio, USA.E-mail : [email protected]

(Received 11 May 2004 ; in revised form 30 May 2004)

ABSTRACT

Great advances have been made recently in the modeling of manufacturing processes that permit the integrationof material behavior with process design and control. The objectives are often to reduce defects, improve partproperties and quality, and to make the manufacturing system more productive. This paper demonstrates someof these advances by providing industrial case histories from the rolling, machining, die casting and forgingprocess areas. Cases traditional finite element modeling with microstructural modeling, phase transformations,thermal and shear softening at high strain rates, solidification modeling and use of statistical regression forprocess optimization. References have been provided in the use of AI techniques for reverse engineering thematerial processes for improved properties and reduced defects. It is shown that accurate physical, mechanicaland thermal modeling of deformation and solidification behavior and the interface conditions are essential tothe optimal use of these advanced models for industrial applications which tend to be difficult in formulation.In doing so, simplifications are often necessary to obtain a satisfactory solution to a complex problem.

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TRANS. INDIAN INST. MET., VOL. 57, NO. 4, AUGUST 2004

depends on the rolled microstructure that is controlledby the finishing temperature. Accurate modeling ofhot rolling therefore requires an integrated approachthat models the microstructural evolution togetherwith the deformation and heat transfer processes.

FEM modeling of the deformation process providesan accurate way of obtaining the thermomechanicalhistory of the workpiece. A three dimensionalEulerian finite element code (ROLPAS) based onrigid-viscoplastic assumption for the material behaviorwas developed at the Ohio State University that canmodel thermo-mechanical changes during rollingdeformation and thermal changes between roll passes,as shown in Fig. 2 1. This software was used alongwith other analytical and knowledge based techniquesto address industrial problems. Examples of theseinclude,

FEM models applied to analyze roll pass designin rod rolling 1-5

Numerical and robust design techniques used toreduce variability in the dimensions and propertiesof rolled rod 6,7

Numerical and fuzzy reasoning techniquesintegrated for optimal design of roll passes forimproved rod quality 8,9

Artificial Neural Networks along with numericaltechniques used to reverse engineer the rollingprocess for finished dimensions andmicrostructure 10,11

Numerical methods integrate with themathematical, physics based models ofmicrostructural evolution for improvedpredictions of metal flow and austenite grainsize 12-19

Numerical models integrate with transformationcurves for improved predictions of properties ofrolled rod after cooling 20, 22.

This paper provides greater details on the approachintegrating microstructural evolution with numericalmethods to predict grain size and changing flow stressduring hot rolling. The rest of the approaches areleft for reader to explore.

2.2 Development of microstructure evolutionmodels

The pioneering work by Sellars and Whiteman 23

demonstrated that semi-empirical equations describingmicrostructural phenomena, such as grain growth andrecrystallization kinetics can be used to predictmetallurgical changes during a hot rolling process.

Fig. 1: The physical processes in a steel rod rolling mill

Fig. 2 : Thermo-mechanical phenomena dominant during multi-pass rolling

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RAJIV SHIVPURI : NUMERICAL MODELING OF MANUFACTURING PROCESSES

At The Ohio State University, microstructureevolution models for vanadium modified ferrite-pearlite microalloyed steel TMS80R were integratedwith the FEM models for process simulations. Tomodel austenite evolution in a thermomechanicalcontrol process, it is necessary to develop the modelsfor grain growth kinetics, static recrystallizationkinetics, metadynamic recrystallization kinetics, andrecrystallized grain size ( rexd ). These models weredeveloped by conducting controlled heating and hotcompression tests on a Gleeble 3500thermomechanical testing machine at DSI Inc. Detailson the testing can be found in Pauskar 12.

2.2.1 Grain growth model

Grain growth using conventional grain growth lawand regression analysis yielded the following graingrowth model for TMS80R

⋅×+=RT

tdd 655826exp1026.1 3250

5(1)

Here, d is the austenite grain size at time t (inmicrons),

0d is the initial grain size (microns), T

is the absolute temperature (K), R is the universalgas constant. To apply this isothermal model undernon-isothermal conditions we used incrementalnumerical computation. In this procedure, the time-temperature cooling (or heating) curve is divided intoseveral small time segments. In each of these segments,the temperature is assumed to be held constant. If theinitial grain size in time segment 1 is 01d , the grainsize at the end of mth segment is given by:

∑=

∆+=

n

i ii

mmt RT

QtKdd1

01 exp (2)

Where Q is the activity coefficient and K is a constant.

2.2.2 Recrystallization model

Most of the microstructural changes in bar rollingare due to the static and metadynamic recrystallizationsphenomena. Double hit compression tests wereconducted for modeling recrystallization kinetics usingstrain, strain rate, temperature, grain size and inter-hit time as the control variables. Details on theexperiments can be found in Pauskar 12. The kineticsfor static and metadynamic recrystallizations weremodeled using an Avrami type relation

X tt

n

= − −

1 0 693

0 5

exp ..

(3)

Where X is the material fraction recrystallized attime t, t0.5 is the time for 50% recrystallization andn is the time exponent which is assumed to be aconstant. The value of n was determined to be 1.46for static recrystallization and 1.0 for metadynamicrecrystallization. Regression analysis on theexperimental data yielded the following models for

Static recrystallization:

×= −−−

RTdt 197000exp1073.1 60.0

0433.078.110

5.0 εε &

(4)

Metadynamic recrystallization:

⋅×= −−−

RTZdt app

230000exp1078.5 6.015.00

00.165.0 ε

(5)

Where

⋅=RT

Zapp197000expε& is the apparent

Zener-Hollomon parameter for the deformation inthe roll gap.

Recrystallized grain size:

Experiments were performed with strain, strain rate,grain size and temperature as the control variables.The following equations were developed to model

recrystallized grain size ( rexd ).

Static Recrystallization:

−⋅⋅⋅= −−

Tddrex

3586exp5.36 58.00

06.0341.0 εε &

(6)

Metadynamic recrystallization:

−⋅⋅⋅= −−

Tddrex

3544exp41.53 39.00

113.072.0 εε &

(7)

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2.2.3 Partial recrystallization in a multi-stagedeformation process

Often during the rolling process, the time in theinterstand is not sufficient for completerecrystallization to occur. In other words, someamount of strain is retained in the microstructurewhen it enters the next deformation pass. Severalapproaches have been proposed to handle partialrecrystallization. One of the approaches is to treatthe microstructure as an aggregate. The retained strainand the effective grain sizes are determined using therule of mixtures:

( )Xret −⋅= 1εε (8)

( ) 01 dXdXd rexeff ⋅−+⋅= (9)

where, X is the fraction recrystallized, retε is theretained strain, effd is the effective grain size, 0dis the initial as heated grain size and rexd is therecrystallized grain size.

The other approach is to treat the recrystallized andunrecrystallized fractions independently (Karhausenand Kopp 24). However, the number of fractions tobe handled increases exponentially, which calls fortremendous amount of computer memory and time.Yanagimoto et al. 25 proposed a variation ofKarhausen’s model. In this approach, the number offractions increases linearly, which requiresconsiderably less memory. However, as with the ruleof mixtures, considerable approximation is involvedand the true behavior of the system is not represented.

Here, three hit compression tests were conducted todetermine the validity of the rule of mixtures. In thethree hit compression tests, the first inter hit timewas kept deliberately short to cause partialrecrystallization. The second hit was followed by athird hit with an inter-hit time between the two. Theamount of recrystallization in the second inter-hittime was measured using the same procedure as wasused in the double hit compression tests. It was foundthat the rule of mixtures shows a better correlationwith the measurements for TMS80R and was henceused in the integrated model.

2.3 Microstructure dependent flow stress model

Flow stress of steel at hot rolling temperatures was

found to be strongly dependent on the microstructure,specifically the austenite grain size in addition toprocess parameters such as strain, strain rate andtemperature.

( )0,,, dTff εεσ &= (10)

A microstructure dependent flow stress model wasdeveloped and integrated into the FEM module. Theflow stress model is capable of modeling themetallurgical phenomena such as strain hardening,dynamic recovery and recrystallization. Figures 3 and4 demonstrate the capability of the flow stress tomodel accurately the work hardening and thermalsoftening processes occurring during plasticdeformation of steels under constant strain rate aswell as changing strain rate conditions. Details aboutthe microstructure dependent flow stress model canbe found in Pauskar et al. 16

2.4 Integrated Model and Validation

The central feature of the integrated system is a threedimensional finite element program ROLPAS forsimulating multi-pass shape rolling. The non-isothermal deformation analysis in ROLPAS is basedon rigid-viscoplastic assumption of the materialbehavior as described earlier and uses eight-nodeisoparametric hexahedral elements. Deformationwithin the roll gap is assumed to be kinematicallysteady. Such an assumption has been successfullyapplied earlier to steady state processes such asextrusion and rolling.

A microstructure evolution module MICON wasdeveloped and integrated into ROLPAS to enablemodeling of austenite evolution. MICON uses thethermomechanical history computed by the FEMmodel in conjunction with microstructure evolutionmodels to determine the evolution of austenite duringhot rolling. The evolving austenite was found tosignificantly affect the flow stress of the materialwhile the material flow affects recrystallizationkinetics. This situation calls for an iterative approachin modeling metal flow and austenite evolution. Forthe first pass, an initial preheated grain size is inputto the program. After deformation and heat transfercomputations for each pass, the microstructureevolution module in conjunction with the heat transfer

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analysis module computes recrystallized fraction andthe austenite grain size at each node in the interstandregion. In the event of complete recrystallization,grain growth after recrystallization becomes importantin determining the recrystallization kinetics of thenext pass. Partial recrystallization is handled usingthe rule of mixtures as described earlier.

The non-integrated approach used in earlier studiesresulted in higher predictions of rolling loads usingFEM. A seven pass rough rolling sequence from aleading steel company was chosen to study the effectof microstructure modeling on the load predictions.The roll pass sequence converts a 15"x15" ingot intoa 12" round bar in seven rough rolling passes.

Measurements of roll loads were made on the rollingmill. The process was simulated using integratedROLPAS first with and then without microstructuremodeling. It was seen that the predictions of therolling loads with microstructure modeling werewithin 10% of the measurements while, thepredictions without microstructure modeling wereconsistently much higher (Fig. 5(a)) 5,26.

Experience with process modeling using FEM hasshown that predictions of material spread are stronglydependent upon the flow stress model. A three passrough rolling schedule being used in a steel companyto convert a 6-5/8"x 6-5/8" square billet to a 5"diameter round billet was chosen to illustrate theeffect of microstructure modeling on the materialflow. Figure 5(b) shows the mesh at the exit of therolls in the second pass as predicted by the finiteelement model with and without microstructuremodeling. A sketch of the actual shape seen at theend of the second pass is also shown. It can be easilyseen that the finite element model withoutmicrostructure modeling grossly under predicts thematerial spread. It also fails to predict the bulgeprofile of the workpiece. On the other hand,predictions of material spread with microstructuremodeling are more accurate and the shape predictedis closer to what is seen in practice.

2.5 Benefits to Industry

The microstructural based numerical model of multi-pass hot rolling and post rolling transformation providethe rolling mills the tools to carryout the followingtasks:

Design and verification of roll pass sequence forgiven product geometry and dimensions. Finishdimensions and temperature are often the designresponse.

Design of thermo-mechanical processing forimproved product properties and quality.Microstructure and final mechanical propertiesare control parameters.

Reduction of product defects such as seams, fins,segregations and cobbles.

Process control for reduced variability and scrap.

Fig. 3 : Effect of temperature on flow stress.

Fig. 4 : Flow stress predictions vs. measurements underchanging strain rates

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Fig. 5 : Effect of microstructure modeling on (a) rolling load and (b) material spread predictions

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3. PHASE TRANSFORMATIONS,THERMAL SOFTENING ANDFRACTURE

3.1 Machining of Titanium Alloys: Application inAerospace Industry

Titanium and its alloys are used extensively inaerospace industry because of their excellentcombination of high strength-to-weight ratio, highelevated temperature strength, high fracture toughness,and exceptional resistance to corrosion. On the otherhand, titanium and its alloys are classified as difficult-to-machine materials due to their inherent propertiessuch as 1) high chemical reactivity and therefore atendency to weld to the cutting tool during machining,thus leading to chipping and premature tool failure;2) low thermal conductivity that prevents heat transferin the material, consequently increasing thetemperature at the tool/workpiece interface affectingthe tool life adversely; 3) high melting temperatureand high strength maintained at elevated temperatureand its low modulus of elasticity impairing itsmachinability.

Increase in cutting speed usually results in rise ofcutting temperature since heat generation per unittime increases. This increase in temperature isdeleterious to the tool life, dimensional accuracy ofthe product or machining efficiency. Extensive toolwear, cyclic loads and segregated chips are oftenobserved in the face milling of titanium slabs leadingto fast tool wear, distortion of work piece surfaceand increased tooling cost. To achieve optimal cuttingconditions for reduced machining times, the cuttingconditions and the tool are changed with the cuttingrequirements, Fig. 6.

Research was initiated in the Laboratory of Excellencefor Machining Technology to study chip segmentationin titanium machining 27-30, development of a diffusionbased tool wear model31, study the effect of thermo-physical properties 32 and to model discontinuouscutting in titanium milling33.

3.2 Effect of temperature on the titanium flow stress

High temperature over the tool/workpiece interfaceis mainly contributed by the heat generated in theworkpiece/chip during the cutting process. It is well

Fig. 6 : Different machining parameters are used to machine a titanium part optimally

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known that the heat generated inside the workpieceis concentrated along the primary deformation zoneand the secondary deformation zones, appearing asthermal energy. A rough estimation of the tool rakeface temperature can be obtained using equation 1134:

21

=ckvhET f ρ (11)

where Tf is the mean temperature over tool rakeface, E is the cutting energy (assuming all cuttingenergy is converted to heat), k is thermal conductivity, is density, c is specific heat, v is cutting speed, and

h is depth of cut.

From the above equation it is seen that the thermalproperties significantly influence the temperature overthe tool/workpiece interface. The temperature variesinversely with the half-power of the change of theproduct of thermal conductivity k, and heat capacityrc. Thus, higher temperatures are to be expected incutting stronger materials (high E) at higher speed,especially if the workpiece material is a poor heatconductor of low density, and low specific heat.

The density of Ti-6Al-4V can be thought as constant,while the thermal conductivity and specific heat varywith temperature. Both capacity and conductivityincrease with temperature 35.

Poor conductivity of the titanium alloys (as comparedto steels) results in a larger portion of the heatgenerated during machining being transferred to thecutting tool, Fig. 8 36. This leads to high tooltemperatures resulting in high tool softening andwear.

Cutting forces and interface pressure generated duringmachining are directly proportional to the flow stressof the workpiece material at the representative thermo-mechanical conditions. During machining the titaniumalloy experiences high strains, very high strain ratesand temperatures close to its melting point. Thisresults in the following material response:

i. Rapid strain hardening at room temperature withstrain softening after a peak flow stress is reached(saturation of slip density in the + phase).

ii. As the temperature is raised due to heatgeneration in the primary and secondary shearzones, both the strain hardening and strainsoftening responses reduce with phasetransformations, with almost rigid-perfectlyplastic behavior above beta transus.

iii. The strain softening of Ti-6Al-4V duringdeformation varies with the change ofmicrostructure and much more marked flowsoftening is observed in microstructurecompared to the + microstructure. Thesoftening rate depends on the volume fraction ofthe and phases present below the transustemperature and on the phase above thistransus.

iv. Strain rate hardening continues at all temperatureswith the strain rate sensitivity increasing at highertemperatures. This increase in sensitivity has amajor influence on propagation of plasticinstability.

Fig. 8 : Energy flow rate into tool vs. thermal conductivityof tool 36.

Fig. 7 : Thermal conductivity and heat capacity of Ti-6Al-4V

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v. Reduction in flow stress with increase intemperature (thermal softening) leads to strainlocalization which in turn causes greaterdeformation in the localized region. Thisaccumulation of deformation eventually leads tomaterial fracture and the segregated chip.

For practical cutting speeds in machining, the averagestrain rate in the primary shear zone lies in the rangeof 103 to 105 /s and effective strain can exceed 3.0.The flow stress model should be able to cover thisrange. In addition, in - titanium alloys, phasetransformation to takes place above transus. Theoriginal flow stress data are modified on the basis ofpublished sources 37-41. Detailed information aboutthe flow behavior of Ti-6Al-4V versus temperatureand strain rate as well as the flow stress at high strainrate and high temperature can be found in these papers.Consequently, in this study, the flow stress responseto changing strain, strain rate and temperature ismodified based on the microstructural changes in thedeformed chip. The detailed procedure can be foundin papers 42, 43. Figure 9 shows schematically thematerial model used in this research. The flowlocalization and the fracture depend on the thermo-mechanical behavior and the microstructure of thetitanium alloy.

3.3 FEM model for orthogonal machining

In this research the cutting process is modeled asorthogonal machining. This simplification of geometryand metal flow permits the process to be assumed a2-dimensional plane strain problem where themovement of the cutting tool is perpendicular to itsstraight cutting edge. A simplified FEM model forcutting tool, workpiece and interface is illustrated inFig. 10.

The material for the cutting tool is tungsten carbide(WC/Co) while the workpiece is titanium alloyTi-6-4. The interface between the chip and tool rakeface is modeled by means of an interface heat transfercoefficient and sliding friction factor. The toolgeometry, cutting process variables and materialproperties of tool and coating are listed in Table 1and Table 2 respectively. Temperature boundarycondition on the tool surface is set as follows:

a. Constant temperature value of 25 °C is assignedto the nodes on the rake face which are not in

Fig. 10: An orthogonal FEM grid model for turning

Fig. 9 : Flow stress of Ti-6Al-4V as a function of strain,strain rate and temperature. Note the substantialsoftening at large values of strain at lower temperatures

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contact with workpiece due to the applied watercoolant on the rake face.

b. Heat exchange with air condition is assigned tothe rest of the nodes on the tool surface. If aspecific node is in touch with the workpieceduring the cutting cycle, heat transfer calculationwill be automatically conducted by the program.Otherwise, the heat exchange with air calculationwill be performed.

Table 1CUTTING CONDITIONS

Variables Value Depth of cut 0.35 mm Rake angle 5o Relief angle 6o Tip radius 0.005 mm

Coating thickness 0.05 mm

Cutting speed 12 m/min, 60 m/min, 120 m/min., 240 m/min., 600

m/min.

Table 2TOOL MATERIAL PROPERTIES

Materials Tool substrate Coating

Elastic modulus 558 (GPa) 672 (GPa)

Poisson’s ratio 0.22 0.22

Thermal conductivity 80 36, 80, 130(W/m/oK) (W/m/oK)

Heat capacity 2.79 106 2.79 106

J/m3/oK J/m3/oK

Thermal expansion 6.8´10-6 (/K) 6.8´10-6 (/K)

3.4 Validation of the Numerical Model

Several assumptions are made for the FEM modelincluding rigid-viscoplastic workpiece, rigid tool, andthe strain rate and temperature dependent flow stress.The model was verified by comparing predictions ofcutting forces and chip morphology (metal flow) withcarefully conducted experiments in the machininglaboratory.

The experiments were conducted on a CNC TurningCenter at cutting speeds of 60, 120 and 240 m/min,feeds of 0.127 and 0.35 mm/rev and depth of cut of2.54 mm. The cutting forces were measured with aKistler dynamometer, Type 9121. Workpiece was aTi-6Al-4V annealed rod. The results of theseexperiments and the model predictions are presentedin Fig. 11. The difference in force magnitudesbetween those measured experimentally and predictedis less than 5% for both the feeds.

Figure 12 compares of chip morphology measuredand predicted by the numerical model. The shapeand the pitch of the serrated chip segments in thesefigures show good geometric resemblance as well asreasonably close dimensional attributes. It should benoted that the original chip collected from the turningtest was a curled chip. The collected chip was thenstraightened and mounted. After etching andpolishing, the chip morphology shown in Fig. 12(a)was obtained from the mounted chip. Thestraightening process increases the distance betweenchip serration and reduces the thickness of the segmentconnecting the serration.


The developed numerical model with phasetransformation implicitly included in the flow stressand fracture is being used to address industrial

Fig. 11: A comparison of measured and predicted cuttingforces at different feed rates and cutting speeds

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Fig. 12: A comparison of chip morphology between experiment (top) and predictions (bottom) at various cutting conditions

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problems such as,

Optimal machining parameters for a givenmaterial, heat treatment and part geometry

Increased material removal rates for minimizingmachining times

Improved workpiece functional attributes suchas surface integrity and precision

Design of cutting tool geometries and materialsfor increased tool lives and reduced tool changes.

4. SOLIDIFICATION PROCESSINGAND POROSITY CONTROL

4.1 Die Casting of Engine Block: Application inAutomotive Industry 44, 45

With the emphasis on light weight cars, automotivecompanies are increasingly using die cast engine blocksfrom high silicon aluminum alloys (Fig. 13). In thesecastings, the main cause of defect is leaker paths incertain critical areas of the castings due tomicroporosity. These leaker defects cause the cylinderblock to fail the pressure leakage test and such castingshave to be discarded as scrap. The aim of this studywas to redesign the gate and optimization of theingate parameters with a focus on minimum airentrapment for minimum gas porosity and betterfilling of thick sections for reduces shrinkage relateddefects.

4.2 Location and Identification of Porosity

Analysis of pressure test results on the die cast andmachined engine blocks indicated that most of theleakage occurred from two locations shown in Fig. 13:Region 1 near the bearing area and Region 2 near thecoolant entry area (the vent area for the die casting).Sections were cut from these locations in the castdies, polished and examined. While Region 1 showedclassical porosity linked to shrinkage due to thermalgradients, Region 2 showed the presence of poreswhich were not spherical, Fig. 14.

The latter pores were analyzed using SEM techniques.It was found that while the composition on the outsideregions of the pores represented the typicalcomposition of the Al 380 die casting alloy, that inthe inner regions showed a high presence of oxygen,Fig. 15. This is an indication of air being trapppedduring the die casting process (poor filling duringmetal injecttion). It was decided to focus on reducingor eliminating air or gas entrapment during metalinjection by optimizing the the metal flow die runnersystem.

4.3 Flow Optimization procedure

The parameters used in this optimization study weregate velocity, fill time and flow angle for the fanand the tangent gates. This simulation study was basedon CastView®, a software developed at The OhioState University with support from NADCA (NorthAmerican Die Casting Association). The designalternatives considered are shown in Fig. 16.

Fig. 13: A five cylinder engine block produced by die casting aluminum. Location of regions of interest: Region 1 near thebearing area, Region 2 near the vent area.

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Fig. 14: Porosity location in the vent region and its relationship to die configuration

A Box-Behnken design array with 15 runs, inclusiveof 3 center runs, was chosen for this three -level /three-factor study, Fig. 16. Simulations wereperformed in CastView for all the runs and the resultswere analyzed with a view for optimization the fillingprocess. An appropriate response variable was chosenwith the objective to obtain a proper fill in which theregion closest to the vent fills last, and the adjoiningareas fill immediately before this region, and so on.A regression model was built with the results of theanalysis. The regression model was maximized usingMicrosoft Excel® software, in keeping with theobjective of maximizing the response (the regionsnear the vents should fill last). The regression equationis as follows,

Response Variable = 2.37523 – 10.123372 A +0.000370338 B – 0.022142558 C + 32.057016 A2+ 0.00001824 B2 – 0.0002299 C2 –0.0131143 AB+ 0.030074282 AC + 0.000019886 BC

Where A refers to the fill time (sec), B refers to thegate velocity (m/s),C refers to the flow angle (degrees)

The range of variation used for the parameters wasas defined in the design array. It was found that theoptimum values for maximum response correspondto the maximum value of the gate velocity, minimumvalue of the fill time and flow angle in the range ofvariation. A runner was designed for the best designalternative using standard NADCA guidelines.

4.4 Comparison of the new design and existingdesign using FLOW3D

A cavity filling simulation using the new gate designparameters was performed using the software packageFlow3D (a finite difference software for fluiddynamics) and compared with simulations performedwith existing gate designs 45. For this simulation thebest design alternative was chosen. Using design

Fig. 15: Analysis of the pore composition using SEM: Note the presense of oxygen inside the pore (picture on the right)

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Fig. 17: The fill pattern in the new design (left) and the fillpattern in the original design (right) 45


This study provided to the die casting industry a

symmetry, a two-cylinder model was used forsimulation as it reasonably represents the fillingcharacteristics of the entire block since cross-flowbetween cylinders is very less.

The results and comparisons of the simulations areshown in Fig. 17. In the simulation of the existingdesign, the runner system is included while in thesimulation of the new design, a runner system hasnot been included. Consequently, in the new designthe metal reaches the gate very fast, whereas in theexisting design the metal reaches the gate only after0.1 sec. So the comparison plots have been made atthe same times that have elapsed after the metalreached the ingate. The figures only show the regionsthat have been filled with metal.

In all the three figures, we can see that in the caseof the new design the filling is faster than the existingingate design case. The bearing areas get filled muchfaster and hence there is more time for the thicksections to solidify and this could lead to reducedshrinkage defects in the region. The vent region andthe adjoining areas also get filled at almost the sametime and hence there is lesser chance of entrappedgas porosity in that region in the new design. Fromthe above comparison it can be seen that the newingate design combined with a larger ingate velocityfavors better filling in the bearing and the vent regions.This will help in the reduction of entrapped gasporosity during filling and shrinkage porosity duringthe solidification stage.

Fig. 16: The geometric parameters of the gate and the design values chosen in the optimization.

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systematic analysis approach to the analysis of porosityand its elimination using computational approaches.

5. FEM AND STATISTICAL METHODS

5.1 Cracking in Cold Extruded Parts: ForgingIndustry 46-48

While cold forging certain automotive drivecomponents in industry, ‘End cracks’ were observedto occur randomly. As the name suggests, they arefound on the front end of the extruded part. Thesecracks are radial and propagate in the longitudinaldirection. They are often visible to the naked eye,showing up after the extrusion stage or duringsubsequent machining operation. An example of anend crack can be seen in Fig. 18(a). These crackslead to significant economic losses as they increasethe scrap volume and the requirement for inspectionof each forged part once they are detected. Forgingcompanies often resort to expensive processes likein-process annealing to reduce the probability ofcracking.

The center of an extruded product can develop cracks(variously known as center-burst, center-cracking,arrowhead-fracture, or chevron-cracking), as shownin Fig. 18(b). These cracks are attributed to a stateof hydrostatic tensile stress (also called secondary

tensile stresses) at the centerline of the deformationzone in the die. This situation is similar to the neckedregion in a uniaxial tensile-test specimen. Thetendency for center cracking increases with increasingdie angles and levels of impurities, and decreaseswith increasing extrusion ratio.

The ‘Counter Shaft’ part (Fig. 18(a)) was the focusof this investigation. The billet material is 8620 steel.The shaft is manufactured by first shearing a billetfrom a rolled rod. Then three stages of extrusion(high ratios) which is followed by one stage ofupsetting. In this particular family of parts, billets oflarger diameter had a greater propensity for endcracking and the percentage of cracked parts reducedgreatly by annealing the billets after the shearingprocess. Almost all cracks originated in the firstextrusion operation. There was a greater tendency tocrack when the burr formed in the shearing processwas large, or if the sheared billet profile was ratheruneven or oblique. Remedies tried in the past includedsawing the billets instead of shearing, using smallerdiameter billets in order to have reduced extrusionratios and annealing and stress relieving. None ofthese remedies were able to deal with the crackingproblem effectively.

There are three types of issues that can be associatedwith this problem:

Fig. 18: Examples of cracking during cold forging-extrusion: (a) End Cracks observed from the outside (b) Chevron internalcracking

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Fig. 20: (a) Standard die and (b) Double reduction die 49

Where: ‘ s – semi-die angles, L ‘s – Landlengths, R – Relief between stages, - Coefficientof friction, r ‘s – Radiuses

i) Die design issues (friction, die angle, land, etc)

ii) Material issues (fracture strength, microstructure,hardness, etc)

iii) Shearing issues (residual stresses, oblique profile,etc)

The last two issues related to pre-forging conditionswhich are difficult to control. Consequently, onlythe design issues were the focus of this investigationwith the goal of developing guidelines for the designof forging-extrusion dies.

A logical hypothesis was presumed to explain endcracking phenomenon during cold extrusion. Thehypothesis can be stated as follows: (refer to Fig. 19)

As the material is relieved out of the die land, dueto elastic recovery, the surface of the extrudate tendsto expand out while the center keeps flowingunimpeded. This differential expansion causes huge,tensile, circumferential stresses to develop close tothe surface, while the center is still being compressedgiving rise to a radial stress gradient. When the tensilehoop stresses close to the surface exceed a criticalvalue, the crack initiates. This crack then propagatedlongitudinally, as more and more material is extruded.

5.2 Finite element investigation

stress raiser causing fracture to occur. This explainsthe random nature of end cracks.

A review of literature showed that many brittlematerials are subject to circumferential (transverse)and longitudinal surface cracking during hydrostaticextrusion. This problem of extruding low-ductilitymaterials was approached in an innovative way bysome researchers at Battelle Columbus Labs 49. Theyestablished that the cracks first developed in the rearsection of the die land, immediately before the exitplane and that the surface cracking resulted fromresidual tensile stresses as the product left the die.The presence of a second small reduction (Fig. 20)prevents cracking by imposing an annular counter-pressure in the extrudate as it exits the first portionof the die. This counters the axial tensile stressesarising from residual stresses, elastic bending andfriction. Prevention of circumferential cracks uponexit from the second portion of the die is believed tobe associated with the favorable permanent change inresidual stresses in the workpiece caused by the secondsmall reduction.

Two FEM simulations 50 were carried out for the

Fig. 19: Elastic unloading of the material as it exits the die49

This fracture hypothesis was validated using Finiteelement Analysis of the extrusion process usingDEFORM 2D v 5.1 50. Simulations were carried outwith elastic-plastic and rigid-plastic material models,the material having elastic-plastic properties showedsignificantly high residual circumferential stresses ascompared to the material with rigid-plastic properties.While the stresses generated were just below thefracture stress of the material in the elastic-plasticcase, the presence of random defects in the materialsuch as seams, segregations, etc. may provide the

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‘Counter Shaft’ part. The first was the conventionaldie with a single reduction, while the second one wasthe new die design with double reduction. The totalreduction in area was kept the same in both the cases(63%). The billet was treated as ‘elastic-plastic’,while the die and punch were treated as rigid bodies.

A comparison of the stresses in the circumferentialdirection (Fig. 21 and Fig. 22) shows a significantreduction (above 50%) in the case with the doubleland (from 103.99 ksi to 45.5 ksi). As expected, thisis due to the compressive stresses developed at thesecond reduction, which counteract the tensile stressesat the first stage. From the simulation results, we canconclude that the double reduction die is a good wayof reducing the circumferential tensile stresses in theworkpiece at the die exit. This helps in dealing withend cracks to a certain extent.

On the other hand, the load requirements on thepress are increased about 23% owing to the presenceof the extra reduction. This might be one of theconstraints in the design process. The otherdisadvantage of this design change is that it may leadto high, tensile axial stresses along the center of theextruded part. This might lead to ‘centerburst’ or‘chevron cracking’.

5.3 Statistical Analysis

It was noted that the decrease in tensile circumferentialstresses (that cause end cracking) was accompaniedby a corresponding increase in the axial stresses (thatcause chevron cracking). Hence, there is a need tooptimize the die design such that the stresses in thematerial at the die exit are kept at a minimum.

The following factors are identified for furtherinvestigation (see Fig. 20): relief between stages (R,inches), die angle (a, degrees), land length at secondstage (L, inches), % reduction at second stage, friction(m). The corner radii being very small have beenneglected in this investigation. Using ‘Design ofExperiments’ (DOE) 52 the above parameters werescreened to see which ones were important for furtherinvestigation. A 252 design was chosen. This resultedin 8 simulation runs. Based on industry practices, thehigh and low values were established for each of theparameters. These values were decided. Thecircumferential stress ( q) at the die exit was theessential response. In addition, the axial stress ( a,which might lead to chevron cracking) was thesecondary response. All the factors were foundsignificant with respect to both these responses andhence were chosen for further investigation.

Once the importance of various parameters wasestablished, a final DOE was carried out for the

Fig. 21: Circumferential stresses at die exit for the die single reduction (left), double reduction (right)

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optimization of the design. The model selected wasa 3-level, five factor DOE. Using a ‘fractionalfactorial’ design, the same experiment was conductedwith a reasonable level of accuracy with 15 runs.The ranges for the parameters were same as thescreening experiment, while the middle value wassimply the average of the low and high levels (seeTable 3). As in the screening experiment, thecircumferential stress ( q) was the main response andthe axial stress ( z) was a secondary response.

Table 3LOW, MIDDLE AND HIGH VALUES FOR THE FACTORS

Parameter Low Middle High(-1) (0) (+1)

Relief Btw Stages (in) 0 .375 0.75

Die angle (degrees) 5 11.75 18.5

Land (in) 0.15 0.325 0.5

Reduction (%) 4 7 10

Friction (m) 0.08 .14 0.2

Using regression analysis, nonlinear equations wereobtained for circumferential stress and axial stress interms of the design variables (factors).

5.4 Optimization of the die design

Using the regression equations and the values of thedesign parameters from common industry knowledgeand practices, the following nonlinear minimizationproblem was formulated. To meet the preliminary

objective of eliminating end cracking in the extrudedshafts, it is necessary to contain the maximumcircumferential stress ( ) and the maximum axialstress ( z) below the fracture strength of the materialin circumferential tension and uniaxial tension,respectively (i.e., < 107.5 ksi and z < 98 ksi).

Minimize:

= (136.19) – (138.74*a) + (0.48*b) +(90.61*c) + (6.59*d) – (1022.8*e) +(43.33*a2) – (1.39*d2) + (496.06*e2) +(7.5*a*d) + (381.23*a*e) + (90.22*d*e)

Subject to:

z = (79.97) + (256.16*a) - (13.78*b) +(31.04*c) - (1.81*d) + (91.79* e) -(225.72* a2) + (0.664* b2) + (0.08*d2) -(0.44*a*b) - (7.03*a*d) + (0.498*d*b) 80

Where the design constraints are:

0 a (relief between stages) 0.75; 3 b (dieangle) 15; 0.05 c (die land ) 0.5 4 d (%reduction ) 10 and 0.08 e (coefficient of friction) 0.2

Using the solver in Microsoft Excel®, the followingoptimum solution (Table 4) to the problem wasobtained:

Table 4OPTIMAL VALUES OF THE DESIGN PARAMETERS

Variable Parameter name Optimal value

a* relief between stages 0.587 in

b* die angle 5.146o

c* die land length 0.05 in

d* % reduction 10 %

e* coefficient of friction 0.08

5.5 Validation of optimal design

The optimal design was incorporated intoDEFORM2D and was tested for consistency (Fig. 22).The predicted and observed values were very muchin agreement, as shown in Table 5. The observed

Fig. 22: Circumferential stress at die exit for the optimaldesign (Max. value: 65.16Ksi, predicted value: 59Ksi)

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and the predicted values deviate by +10.44 % for and by -7.27 % for z.

Table 5OPTIMAL VALUES OF THE STRESSES AND THEIR

FACTORS OF SAFETY

Variable Optimal Value Fracture Factor ofFrom From stress(2) SafetyEquation FEA (2) / (1)

* (Circ) 59 Ksi 65 Ksi 1.822 107.5 Ksi

z* 80 Ksi 74 Ksi 1.225 98 Ksi

5.6 Die design guidelines

To provide flexibility to the die designer, a ‘range’has to be provided for each die design parameter.This range will give the die designer the requiredflexibility while choosing the values of the die designparameters, while maintaining the stresses (both axialand circumferential) well below their minimum. InTable 4, the lower limit is the smallest value that theparameter can take while holding all other parametersfixed and still satisfy the constraints. The upper limitis the greatest value. Table 6 shows the safe rangesfor each parameter, determined by sensitivity analysisand rounded off.

Table 6RANGES FOR THE DIE DESIGN PARAMETERS AND

THEIR EFFECT ON THE STRESSES

Parameter Safe range

relief between stages 0.55 in – 0.75 in

die angle 5o – 8o

die land 0.05 in - 0.2 in

% reduction 8% - 10%

friction coefficient(m) 0.08 - 0.15

Based on the literature on ductile fracture of materials,the forming limit diagram (Fig. 23) for 8620 steelwas constructed. These guidelines are meant to beused with Finite Element Analysis. When a simulationis conducted for 8620 steel, the fracture limits can bedetermined from the above figure. The area O-A-B-C is the safe operating zone.

Various stress states were looked into at the differentstages of extrusion. A comparison of the stress stateswas thus made between the single reduction die(original design) and double reduction die (optimaldesign). A ‘point tracking’ routine was undertakenusing DEFORM2D. One typical point on the billet,in the area where stress is maximum, was selectedand its stress profile was tracked for the entireextrusion process. This was done for both the singleand double reduction die.

Fig. 23: Forming limit diagram for extrusion of the counter shaft

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It was found that both single and double reductiondies follow almost similar paths for circumferentialstress, since the nature of the deformation is similar.Also the axial stress paths are almost similar for thefirst reduction and emergence from the first land.Since the percentage reduction is lesser at the firststage of the double reduction die as compared to thesingle reduction die, there are some tensile axialstresses at the center in the case of the former.

Industrial trials with the new double reduction diedesign eliminated the cracks in the typical trial of10,000 parts. This validated the design predictions.

7. CONCLUSIONS

Advances in numerical techniques along with accuratemodeling of material behavior have made it possibleto analyze and optimize deformation and solidificationprocesses for significant improvement in processquality and productivity. Recently, these techniqueshave been augmented by AI tools such as fuzzyreasoning and ANNs that enable incorporation ofdomain knowledge. In addition, SPC and robustdesign techniques have been integrated to reducevariability and to improve product properties. Thecollaborative industrial-governmental-academicresearch being conducted at the ManufacturingResearch Group, The Ohio State University hasresulted in significant cost reduction, and quality andproductivity improvements for the participatingindustry. The cases presented in this paper are onlya few examples of the application of these advancedtheoretical techniques to the steel mills and theaerospace and automotive manufacturers (die castingand forging). The goal of this paper was todemonstrate the few successes of this collaborativeeffort.

ACKNOWLEDGMENTS

The support provided by the member companies(Timken, Inland steel and Chaparral steel) of theConsortium for the Advancement of RollingTechnology, by the Volvo Car Company, by theSikorsky Aircraft Corporation, the MetaldyneCorporation and by the Dynamic Systems Incorporated(DSI) is gratefully acknowledged. The author alsowishes to acknowledge the support from the

Department of Energy and the UES, Inc; from SFTC,Columbus OH, for providing FEA software DE-FORM_2DTM; and from TechSolve, Cincinnati OHfor providing help with experiments for the machiningresearch. The author finally expresses his appreciationto Praveen Pauskar, Jiang Hua, Shivakumar Kannan,Venkat Sankararaman, Ashish Pabalkar, PeeyushMittal and Satish Kini, and the former and currentresearch associates at The Ohio State University, fortheir hard work and efforts.

REFERENCES

1. Kim N, Lee S M, Shin W, and Shivpuri R, J. of Engr.for Industry, 114 (1992) pp 329-335.

2. Shin W, Lee S M, Shivpuri R, and Altan T, J. Matls.Proc. Tech., 33(1-2) (1992) pp 141-154.

3. Lee S M, Shin W, and Shivpuri R, Int. J. MachineTools and Manufacture, 32(3) (1992) pp. 315-327.

4. Shivpuri R, Shin W, and Mehrotra R, J. of Matls. andManufac, Trans. Society of Automotive Engineers,(1992).

5. Sawamiphakdi K, Ives J E, Damm E B, Shivpuri R,and Pauskar P, Steel Rolling ’98, Seventh Int. Conf. onSteel Rolling, Tokyo, Japan, (1998).

6. Yoshimura K, Kini S, and Shivpuri R, Trans. NAMRI/SME, Society of Manufacturing Engineers, XXV (1997)pp 55-60.

7. Kini S, and Shivpuri R, Proc. 40th MWSP Conf., Ironand Steel Society, Pittsburgh, PA, (1998).

8. Shivpuri R, and Kini S, Proc. 39th MWSP Conference,Iron & Steel Society, Indianapolis, IN, (1997).

9. Kini S, and Shivpuri R, Iron and Steel Engineer, Ironand Steel Society, (2001).

10. Shivpuri R, Kini S, and Ji M, Proc. 8th Int. Conf. onSteel Rolling & 44th MWSP, Iron and Steel Society,Orlando, FL, (2002).

11. Ji M, Kini S, and Shivpuri R., Trans. NAMRI/SME,XXXI (2003) p. 475.

12. Pauskar P, Shivpuri R, Cho H, and Kim N, Trans.NAMRI/SME, Society of Manufacturing Engineers, XXV(1997) pp. 67-74.

13. Pauskar P, Phadke S, and Shivpuri R, Proc. 39th MWSPConference, Iron & Steel Society, Indianapolis, IN,(1997).

14. Pauskar P, and Shivpuri R, Proc. 40th MWSP Conf.,

365


Iron and Steel Society, Pittsburgh, PA, (1998).

15. Pauskar P, and Shivpuri R, Trans.of NAMRI/SME,XXVII (1999) pp.61-67.

16. Pauskar P, and Shivpuri R, Annals of the CIRP, 48(1),(1999) p. 191- 194.

17. Pauskar P, and Shivpuri R, Advanced Technology ofPlasticity, Proc. 6th Int. Conf. Tech. Plasticity,Nuremburg, pp. 1967, 1999.

18. Kini S, and Shivpuri R, Proc. 42nd MWSP Conf., Ironand Steel Society, Ontario, Canada, (2000).

19. Shivpuri R, Pauskar P, and Kini S, Proc. of jointJSME/ ASME Int. Conf. on Materials and Processing,Honolulu, Hawaii, (2002).

20. Pauskar P, Phadke S, and Shivpuri R, Trans. NAMRI/SME, Society of Manufacturing Engineers, XXVI (1998)pp. 85-90.

21. Kini S, Pauskar P, and Shivpuri R, Proc. 22nd ForgingIndustry Technical Conference, Lake Geneva, WI, (1999).

22. Phadke S, Pauskar P, and Shivpuri R, in print, J.Matls. Process. Tech, (2004).

23. Sellars C M, and Whiteman J A, Metal Science, March-(1979) pp. 187-194.

24. Karhausen K, and Kopp R, Proceedings of theInternational Symposium on Mathematical Modeling ofHot Rolling of Steel, (1990) 99-118.

25. Yanagimoto J, Karhausen K, Brand A J, and Kopp R,Proceedings of the 1995 Japanese Spring Conferencefor the Technology of Plasticity, (1995) 329-331.

26. Pauskar P, Damm B, Shivpuri R, Phadke S,Sawamiphakdi, K, and Ives, J, Proceedings of the 39thMWSPConf., ISS, 35 (1997).

27. Shivpuri R, Hua J, Mittal P, and Srivastava A, Annalsof CIRP, 50(1) (2002).

28. Hua J, Mittal P, and Shivpuri R, Proc. 7th ICTP, Int.Conf. on Technology of Plasticity, Yokohama, Japan,(2002).

29. Hua J, and Shivpuri R, In print J. of MaterialsProcessing Tech., (2004).

30. Hua J, and Shivpuri R, Accepted J. of Engr. Matls.and Tech., (2004).

31. Umbrello D, Hua J, and Shivpuri R, ESAFORM 2004,Proc. 7th Esaform Conf. on Material Forming,Trondheim, Norway, (2004) pp 741-744.

32. Hua J, and Shivpuri R, Proceedings of the NSF Workshop

on Research Needs in Thermal Aspects of Metal RemovalProcesses, Ed. Ranga Komanduri, Stillwater, OK,(2003).

33. Hua J, Mittal P, Shivpuri R, and Srivastava A, Proc.6th CIRP International Workshop on Modeling ofMachining Operations, McMaster University, Ontario,Canada, (2003).

34. Schey J A, Introduction to Manufacturing Processes,3rd Edition, McGraw-Hill, (2000).

35. Maekawa K, Nakano Y, and Kitagawa T,JSME International J. Series C, 39(4) (1996)pp. 864-870.

36. Lee W S, and Lin C F, J. Mater. Proc. Tech., 75(1998) pp. 127-136.

37. Gartside M B, The Minerals, Metals & Materials Society,(1997) 101-108

38. Usui E, Obikawa T, and Shirakashi T, Proc. 5th Int.Conf. Production Eng., Tokyo, (1984) pp. 233-239

39. Lee D, J. Eng. Ind., 107(1) (1985) pp. 55-63.

40. Semiatin S L, Lahoti G D, and Oh S I, Plenum Press,New York, (1983) pp. 119-159.

41. Shivpuri R, Hua J, Mittal, P, Srivastava, A K, Annalsof CIRP, 51(1) (2002) 71-74.

42. Hua J, Shivpuri R, Proceedings of the 9thISPE International Conference on ConcurrentEngineering, Cranfield, United Kingdom, (2002)pp. 357-365.

43. Sandstrom D R, and Hodowany J N, Machining Scienceand Technology, 2(2) (1998) pp. 343-353.

44. Kannan, S., Sankararaman, V. and Shivpuri, R., Trans.NAMRI/SME, Society of Manufacturing Engineers,XXVIII (2000) pp. 87-92.

45. Shivpuri R, Sankararaman V, and Kulkarni K, Trans.of NADCA, 2001 Die Casting Congress and Expo,Cincinnati, (2001) pp. 143- 150.

46. Shivpuri R, Pabalkar A, and Kini S, J. of EngineeringManufacture, Proc. Inst. Mech. Engr., Part B, B-08600,(2001) pp. 1377- 1384.

47. Pabalkar A, Kini S, and Shivpuri R, Trans. NAMRI/SME, Society of Manufacturing Engineers, XXVIII(2000) pp. 63-68.

48. Pabalkar A, Shivpuri R, Proc. 23rd Forging IndustryTechnical Conference, Reno, NV. (2001).

49. Hydrostatic Extrusion, Metals Handbook, American

366


Society of Metals, Ninth edition, Forming and Forging,14, pp. 327-329.

50. DEFORM Users Manual, Scientific FormingTechnologies Corporation, (1994).

51. Pabalkar A, Investigation of end cracking in extruded

parts using finite element analysis and statistical methods,M.S. Thesis, The Ohio State University, (1999).

52. Montgomery D C, Design and analysis of experiments,John Wiley and Sons, 2nd edition, (1984).

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