advances in numerical modeling of manufacturing processes

Trans. Indian Inst. Met. 

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

TP 1899 

ADVANCES IN NUMERICAL MODELING OF 

MANUFACTURING PROCESSES: APPLICATION TO 

STEEL, AEROSPACE AND AUTOMOTIVE 

INDUSTRIES 

Rajiv Shivpuri 

Professor and Director, Manufacturing Research Group 

The Ohio State University, Columbus, Ohio, USA. 

E-mail : shivpuri.1@osu.edu 

(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 integration 

of material behavior with process design and control. The objectives are often to reduce defects, improve part 

properties and quality, and to make the manufacturing system more productive. This paper demonstrates some 

of these advances by providing industrial case histories from the rolling, machining, die casting and forging 

process 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 for 

process optimization. References have been provided in the use of AI techniques for reverse engineering the 

material processes for improved properties and reduced defects. It is shown that accurate physical, mechanical 

and thermal modeling of deformation and solidification behavior and the interface conditions are essential to 

the 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. 

1. INTRODUCTION 

Numerical modeling is increasingly being used in the 

design and optimization of manufacturing processes 

for the higher quality of the product and improved 

production yields. Advances in numerical modeling 

of material behavior, efficient computational 

algorithms, better representation of mechanical and 

thermal interfaces, and advances in computer hardware 

and storage devices have enabled complex software 

to be used for process design and optimization. 

Several case histories are included in this paper to 

demonstrate the application of numerical models to 

problems relevant to the industrial members of the 

Manufacturing Research Group at the Ohio State 

University. Selected case histories are from the steel 

mills, the forging industry, the die casting industry 

and the machine shops. Many of these case histories 

are applications of numerical models together with 

heuristic or domain knowledge to improve process 

and die designs, and to reduce defects during 

production. These tools and approaches are necessary 

to produce high quality products, and to engineer the 

production systems for high productivity and quick 

response to customer needs. 

2. HOT DEFORMATION WITH 

MICROSTRUCTURE EVOLUTION 

2.1 Hot Rolling of Bars: Application in Steel Mills 

Recent emphasis on manufacturing rolled products to 

property specifications has resulted in researchers 

trying to use thermomechanical history to model 

microstructural evolution during the rolling process. 

A typical material conversion process in rolling mills 

consists of strand casting, hot rolling of the strands 

into rolled rods, and shearing of rods into billets that 

are converted to discrete parts in the forging process, 

Fig. 1. Often the forgeability of the rolled rod

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

demonstrated that semi-empirical equations describing 

• Numerical and robust design techniques used to 

microstructural phenomena, such as grain growth and 

reduce variability in the dimensions and properties 

recrystallization kinetics can be used to predict 

of rolled rod 6,7 metallurgical changes during a hot rolling process. 

• Numerical and fuzzy reasoning techniques 

integrated for optimal design of roll passes for 

improved rod quality 8,9 

• Artificial Neural Networks along with numerical 

techniques used to reverse engineer the rolling 

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

process for finished dimensions and 

depends on the rolled microstructure that is controlled microstructure 10,11 

by the finishing temperature. Accurate modeling of 

• Numerical methods integrate with the 

hot rolling therefore requires an integrated approach 

mathematical, physics based models of 

that models the microstructural evolution together 

microstructural evolution for improved 

with the deformation and heat transfer processes. 

predictions of metal flow and austenite grain 

FEM modeling of the deformation process provides size 12-19 

an accurate way of obtaining the thermomechanical 

• Numerical models integrate with transformation 

history of the workpiece. A three dimensional 

curves for improved predictions of properties of 

Eulerian finite element code (ROLPAS) based on 

rolled rod after cooling 20, 22 . 

rigid-viscoplastic assumption for the material behavior 

was developed at the Ohio State University that can 

model thermo-mechanical changes during rolling 

deformation and thermal changes between roll passes, 

as shown in Fig. 2 1 . This software was used along 

with other analytical and knowledge based techniques 

This paper provides greater details on the approach 

integrating microstructural evolution with numerical 

methods to predict grain size and changing flow stress 

during hot rolling. The rest of the approaches are 

left for reader to explore. 

to address industrial problems. Examples of these 

include, 

2.2 Development of microstructure evolution 

models 

• FEM models applied to analyze roll pass design 

in rod rolling 1-5 

The pioneering work by Sellars and Whiteman 23 

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

346

RAJIV SHIVPURI : NUMERICAL MODELING OF MANUFACTURING PROCESSES 

d 0 

At The Ohio State University, microstructure 

evolution models for vanadium modified ferritepearlite 

microalloyed steel TMS80R were integrated 

with the FEM models for process simulations. To 

model austenite evolution in a thermomechanical 

control process, it is necessary to develop the models 

for grain growth kinetics, static recrystallization 

kinetics, metadynamic recrystallization kinetics, and 

recrystallized grain size ( d 

rex 

). These models were 

developed by conducting controlled heating and hot 

compression tests on a Gleeble 3500 

thermomechanical testing machine at DSI Inc. Details 

on the testing can be found in Pauskar 12 . 

2.2.1 Grain growth model 

Grain growth using conventional grain growth law 

and regression analysis yielded the following grain 

growth model for TMS80R 

5 5 

32 ⎛ 655826 ⎞ 

d = d0 

+ 1.26× 

10 t ⋅exp⎜ 

⎟ (1) 

⎝ RT ⎠ 

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

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

is the absolute temperature (K), R is the universal 

gas constant. To apply this isothermal model under 

non-isothermal conditions we used incremental 

numerical computation. In this procedure, the timetemperature 

cooling (or heating) curve is divided into 

several small time segments. In each of these segments, 

the temperature is assumed to be held constant. If the 

initial grain size in time segment 1 is d 

01 

, the grain 

size at the end of m th segment is given by: 

n 

m m 

⎛ Q ⎞ 

dt 

= d01 + K∑∆ti 

exp ⎜ 

⎟ 

(2) 

i= 

1 ⎝ RTi 

⎠ 

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

2.2.2 Recrystallization model 

Most of the microstructural changes in bar rolling 

are due to the static and metadynamic recrystallizations 

phenomena. Double hit compression tests were 

conducted for modeling recrystallization kinetics using 

strain, strain rate, temperature, grain size and interhit 

time as the control variables. Details on the 

experiments can be found in Pauskar 12 . The kinetics 

for static and metadynamic recrystallizations were 

modeled using an Avrami type relation 

n 

⎛ ⎛ t ⎞ ⎞ 

X = 1 −exp −0. 

693 

⎜ 

⎜ ⎟ 

⎝ ⎝ t ⎠ ⎟ 

(3) 

05 . ⎠ 

Where X is the material fraction recrystallized at 

time t, t 0.5 

is the time for 50% recrystallization and 

n is the time exponent which is assumed to be a 

constant. The value of n was determined to be 1.46 

for static recrystallization and 1.0 for metadynamic 

recrystallization. Regression analysis on the 

experimental data yielded the following models for 

Static recrystallization: 

t 

= 1.73× 

10 

−10 

−1.78 

−0.433 

0.5 

ε ε 

Metadynamic recrystallization: 

−6 

− 

t0.5 

= 5.78× 

10 ε 

1.00 

& 

d 

0.15 

0 

Z 

d 

0.60 

0 

−0.6 

app 

⎛197000 

⎞ 

exp⎜ 

⎟ 

⎝ RT ⎠ 

(4) 

⎛ 230000 ⎞ 

⋅ exp⎜ 

⎟ 

⎝ RT ⎠ 

(5) 

⎛197000 

⎞ 

Where Z app 

= ε& ⋅ exp⎜ 

⎟ is the apparent 

⎝ RT ⎠ 

Zener-Hollomon parameter for the deformation in 

the 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 ( d ). 

Static Recrystallization: 

⎛ ⎞ 

= ⋅ 

−0.341 

⋅ 

−0.06 

0.58 3586 

d rex 

36.5 ε & ε ⋅ d 

0 

exp⎜ 

− ⎟ 

⎝ T ⎠ 

(6) 

Metadynamic recrystallization: 

⎛ ⎞ 

= ⋅ 

−0.72 

⋅ 

−0.113 

0.39 3544 

d rex 

53.41 ε & ε ⋅ d 

0 

exp⎜ 

− ⎟ 

⎝ T ⎠ 

(7) 

rex 

347


2.2.3 Partial recrystallization in a multi-stage 

deformation process 

Often during the rolling process, the time in the 

interstand is not sufficient for complete 

recrystallization to occur. In other words, some 

amount of strain is retained in the microstructure 

when it enters the next deformation pass. Several 

approaches have been proposed to handle partial 

recrystallization. One of the approaches is to treat 

the microstructure as an aggregate. The retained strain 

and the effective grain sizes are determined using the 

rule of mixtures: 

ε 

ret 

= ε ⋅( 1− X ) 

(8) 

d 

eff 

( 1− 

X ) ⋅ d0 

= X ⋅ d + 

(9) 

rex 

where, X is the fraction recrystallized, ε ret 

is the 

retained strain, d 

eff is the effective grain size, d 

0 

is the initial as heated grain size and d rex 

is the 

recrystallized grain size. 

The other approach is to treat the recrystallized and 

unrecrystallized fractions independently (Karhausen 

and Kopp 24 ). However, the number of fractions to 

be handled increases exponentially, which calls for 

tremendous amount of computer memory and time. 

Yanagimoto et al. 25 proposed a variation of 

Karhausen’s model. In this approach, the number of 

fractions increases linearly, which requires 

considerably less memory. However, as with the rule 

of mixtures, considerable approximation is involved 

and the true behavior of the system is not represented. 

Here, three hit compression tests were conducted to 

determine the validity of the rule of mixtures. In the 

three hit compression tests, the first inter hit time 

was kept deliberately short to cause partial 

recrystallization. The second hit was followed by a 

third hit with an inter-hit time between the two. The 

amount of recrystallization in the second inter-hit 

time was measured using the same procedure as was 

used in the double hit compression tests. It was found 

that the rule of mixtures shows a better correlation 

with the measurements for TMS80R and was hence 

used 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 to 

process parameters such as strain, strain rate and 

temperature. 

f 

( ε , & ε , T, 

d ) 

σ = f 

(10) 

0 

A microstructure dependent flow stress model was 

developed and integrated into the FEM module. The 

flow stress model is capable of modeling the 

metallurgical phenomena such as strain hardening, 

dynamic recovery and recrystallization. Figures 3 and 

4 demonstrate the capability of the flow stress to 

model accurately the work hardening and thermal 

softening processes occurring during plastic 

deformation of steels under constant strain rate as 

well as changing strain rate conditions. Details about 

the microstructure dependent flow stress model can 

be found in Pauskar et al. 16 

2.4 Integrated Model and Validation 

The central feature of the integrated system is a three 

dimensional finite element program ROLPAS for 

simulating multi-pass shape rolling. The nonisothermal 

deformation analysis in ROLPAS is based 

on rigid-viscoplastic assumption of the material 

behavior as described earlier and uses eight-node 

isoparametric hexahedral elements. Deformation 

within the roll gap is assumed to be kinematically 

steady. Such an assumption has been successfully 

applied earlier to steady state processes such as 

extrusion and rolling. 

A microstructure evolution module MICON was 

developed and integrated into ROLPAS to enable 

modeling of austenite evolution. MICON uses the 

thermomechanical history computed by the FEM 

model in conjunction with microstructure evolution 

models to determine the evolution of austenite during 

hot rolling. The evolving austenite was found to 

significantly affect the flow stress of the material 

while the material flow affects recrystallization 

kinetics. This situation calls for an iterative approach 

in modeling metal flow and austenite evolution. For 

the first pass, an initial preheated grain size is input 

to the program. After deformation and heat transfer 

computations for each pass, the microstructure 

evolution module in conjunction with the heat transfer 

348


Measurements of roll loads were made on the rolling 

mill. The process was simulated using integrated 

ROLPAS first with and then without microstructure 

modeling. It was seen that the predictions of the 

rolling loads with microstructure modeling were 

within 10% of the measurements while, the 

predictions without microstructure modeling were 

consistently much higher (Fig. 5(a)) 5,26 . 

Fig. 3 : Effect of temperature on flow stress. 

Experience with process modeling using FEM has 

shown that predictions of material spread are strongly 

dependent upon the flow stress model. A three pass 

rough rolling schedule being used in a steel company 

to convert a 6-5/8"x 6-5/8" square billet to a 5" 

diameter round billet was chosen to illustrate the 

effect of microstructure modeling on the material 

flow. Figure 5(b) shows the mesh at the exit of the 

rolls in the second pass as predicted by the finite 

element model with and without microstructure 

modeling. A sketch of the actual shape seen at the 

end of the second pass is also shown. It can be easily 

seen that the finite element model without 

microstructure modeling grossly under predicts the 

material spread. It also fails to predict the bulge 

profile of the workpiece. On the other hand, 

predictions of material spread with microstructure 

modeling are more accurate and the shape predicted 

is closer to what is seen in practice. 

2.5 Benefits to Industry 

Fig. 4 : Flow stress predictions vs. measurements under 

changing strain rates 

analysis module computes recrystallized fraction and 

the austenite grain size at each node in the interstand 

region. In the event of complete recrystallization, 

grain growth after recrystallization becomes important 

in determining the recrystallization kinetics of the 

next pass. Partial recrystallization is handled using 

the rule of mixtures as described earlier. 

The non-integrated approach used in earlier studies 

resulted in higher predictions of rolling loads using 

FEM. A seven pass rough rolling sequence from a 

leading steel company was chosen to study the effect 

of microstructure modeling on the load predictions. 

The roll pass sequence converts a 15"x15" ingot into 

a 12" round bar in seven rough rolling passes. 

The microstructural based numerical model of multipass 

hot rolling and post rolling transformation provide 

the rolling mills the tools to carryout the following 

tasks: 

• Design and verification of roll pass sequence for 

given product geometry and dimensions. Finish 

dimensions and temperature are often the design 

response. 

• Design of thermo-mechanical processing for 

improved product properties and quality. 

Microstructure and final mechanical properties 

are control parameters. 

• Reduction of product defects such as seams, fins, 

segregations and cobbles. 

• Process control for reduced variability and scrap. 

349


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

350


3. PHASE TRANSFORMATIONS, 

THERMAL SOFTENING AND 

FRACTURE 

3.1 Machining of Titanium Alloys: Application in 

Aerospace Industry 

Titanium and its alloys are used extensively in 

aerospace industry because of their excellent 

combination of high strength-to-weight ratio, high 

elevated temperature strength, high fracture toughness, 

and exceptional resistance to corrosion. On the other 

hand, titanium and its alloys are classified as difficultto-machine 

materials due to their inherent properties 

such as 1) high chemical reactivity and therefore a 

tendency to weld to the cutting tool during machining, 

thus leading to chipping and premature tool failure; 

2) low thermal conductivity that prevents heat transfer 

in the material, consequently increasing the 

temperature at the tool/workpiece interface affecting 

the tool life adversely; 3) high melting temperature 

and high strength maintained at elevated temperature 

and its low modulus of elasticity impairing its 

machinability. 

Increase in cutting speed usually results in rise of 

cutting temperature since heat generation per unit 

time increases. This increase in temperature is 

deleterious to the tool life, dimensional accuracy of 

the product or machining efficiency. Extensive tool 

wear, cyclic loads and segregated chips are often 

observed in the face milling of titanium slabs leading 

to fast tool wear, distortion of work piece surface 

and increased tooling cost. To achieve optimal cutting 

conditions for reduced machining times, the cutting 

conditions and the tool are changed with the cutting 

requirements, Fig. 6. 

Research was initiated in the Laboratory of Excellence 

for Machining Technology to study chip segmentation 

in titanium machining 27-30 , development of a diffusion 

based tool wear model 31 , study the effect of thermophysical 

properties 32 and to model discontinuous 

cutting in titanium milling 33 . 

3.2 Effect of temperature on the titanium flow stress 

High temperature over the tool/workpiece interface 

is mainly contributed by the heat generated in the 

workpiece/chip during the cutting process. It is well 

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

351


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

known that the heat generated inside the workpiece 

is concentrated along the primary deformation zone 

and the secondary deformation zones, appearing as 

thermal energy. A rough estimation of the tool rake 

face temperature can be obtained using equation 11 34 : 

1 2 

⎛ vh ⎞ 

T f 

= E⎜ 

⎟ 

(11) 

⎝ k ρ c ⎠ 

where T f 

is the mean temperature over tool rake 

face, E is the cutting energy (assuming all cutting 

energy 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 thermal 

properties significantly influence the temperature over 

the tool/workpiece interface. The temperature varies 

inversely with the half-power of the change of the 

product of thermal conductivity k, and heat capacity 

rc. Thus, higher temperatures are to be expected in 

cutting stronger materials (high E) at higher speed, 

especially if the workpiece material is a poor heat 

conductor 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 vary 

with temperature. Both capacity and conductivity 

increase with temperature 35 . 

Poor conductivity of the titanium alloys (as compared 

to steels) results in a larger portion of the heat 

generated during machining being transferred to the 

cutting tool, Fig. 8 36 . This leads to high tool 

temperatures resulting in high tool softening and 

wear. 

Fig. 8 : Energy flow rate into tool vs. thermal conductivity 

of tool 36 . 

Cutting forces and interface pressure generated during 

machining are directly proportional to the flow stress 

of the workpiece material at the representative thermomechanical 

conditions. During machining the titanium 

alloy experiences high strains, very high strain rates 

and temperatures close to its melting point. This 

results in the following material response: 

i. Rapid strain hardening at room temperature with 

strain softening after a peak flow stress is reached 

(saturation of slip density in the + phase). 

ii. 

As the temperature is raised due to heat 

generation in the primary and secondary shear 

zones, both the strain hardening and strain 

softening responses reduce with phase 

transformations, with almost rigid-perfectly 

plastic behavior above beta transus. 

iii. The strain softening of Ti-6Al-4V during 

deformation varies with the change of 

microstructure and much more marked flow 

softening is observed in microstructure 

compared to the + microstructure. The 

softening rate depends on the volume fraction of 

the and phases present below the transus 

temperature and on the phase above this 

transus. 

iv. Strain rate hardening continues at all temperatures 

with the strain rate sensitivity increasing at higher 

temperatures. This increase in sensitivity has a 

major influence on propagation of plastic 

instability. 

352


v. Reduction in flow stress with increase in 

temperature (thermal softening) leads to strain 

localization which in turn causes greater 

deformation in the localized region. This 

accumulation of deformation eventually leads to 

material fracture and the segregated chip. 

For practical cutting speeds in machining, the average 

strain rate in the primary shear zone lies in the range 

of 103 to 105 /s and effective strain can exceed 3.0. 

The flow stress model should be able to cover this 

range. In addition, in - titanium alloys, phase 

transformation to takes place above transus. The 

original flow stress data are modified on the basis of 

published sources 37-41 . Detailed information about 

the flow behavior of Ti-6Al-4V versus temperature 

and strain rate as well as the flow stress at high strain 

rate and high temperature can be found in these papers. 

Consequently, in this study, the flow stress response 

to changing strain, strain rate and temperature is 

modified based on the microstructural changes in the 

deformed chip. The detailed procedure can be found 

in papers 42, 43 . Figure 9 shows schematically the 

material model used in this research. The flow 

localization and the fracture depend on the thermomechanical 

behavior and the microstructure of the 

titanium alloy. 

3.3 FEM model for orthogonal machining 

In this research the cutting process is modeled as 

orthogonal machining. This simplification of geometry 

and metal flow permits the process to be assumed a 

2-dimensional plane strain problem where the 

movement of the cutting tool is perpendicular to its 

straight cutting edge. A simplified FEM model for 

cutting tool, workpiece and interface is illustrated in 

Fig. 10. 

Fig. 9 : Flow stress of Ti-6Al-4V as a function of strain, 

strain rate and temperature. Note the substantial 

softening at large values of strain at lower temperatures 

The material for the cutting tool is tungsten carbide 

(WC/Co) while the workpiece is titanium alloy 

Ti-6-4. The interface between the chip and tool rake 

face is modeled by means of an interface heat transfer 

coefficient and sliding friction factor. The tool 

geometry, cutting process variables and material 

properties of tool and coating are listed in Table 1 

and Table 2 respectively. Temperature boundary 

condition on the tool surface is set as follows: 

a. Constant temperature value of 25 °C is assigned 

to the nodes on the rake face which are not in 

353 

Fig. 10: An orthogonal FEM grid model for turning


contact with workpiece due to the applied water 

coolant on the rake face. 

b. Heat exchange with air condition is assigned to 

the rest of the nodes on the tool surface. If a 

specific node is in touch with the workpiece 

during the cutting cycle, heat transfer calculation 

will be automatically conducted by the program. 

Otherwise, the heat exchange with air calculation 

will be performed. 

Variables 

Depth of cut 

Rake angle 

Relief angle 

Tip radius 

Coating thickness 

Cutting speed 

Table 1 

CUTTING CONDITIONS 

Value 

0.35 mm 

5 o 

6 o 

0.005 mm 

0.05 mm 

12 m/min, 60 m/min, 120 

m/min., 240 m/min., 600 

m/min. 

Table 2 

TOOL MATERIAL PROPERTIES 

Materials Tool substrate Coating 

Elastic modulus 558 (GPa) 672 (GPa) 

The experiments were conducted on a CNC Turning 

Center at cutting speeds of 60, 120 and 240 m/min, 

feeds of 0.127 and 0.35 mm/rev and depth of cut of 

2.54 mm. The cutting forces were measured with a 

Kistler dynamometer, Type 9121. Workpiece was a 

Ti-6Al-4V annealed rod. The results of these 

experiments and the model predictions are presented 

in Fig. 11. The difference in force magnitudes 

between those measured experimentally and predicted 

is less than 5% for both the feeds. 

Figure 12 compares of chip morphology measured 

and predicted by the numerical model. The shape 

and the pitch of the serrated chip segments in these 

figures show good geometric resemblance as well as 

reasonably close dimensional attributes. It should be 

noted that the original chip collected from the turning 

test was a curled chip. The collected chip was then 

straightened and mounted. After etching and 

polishing, the chip morphology shown in Fig. 12(a) 

was obtained from the mounted chip. The 

straightening process increases the distance between 

chip serration and reduces the thickness of the segment 

connecting the serration. 


The developed numerical model with phase 

transformation implicitly included in the flow stress 

and fracture is being used to address industrial 

Poisson’s ratio 0.22 0.22 

Thermal conductivity 80 36, 80, 130 

(W/m/ o K) (W/m/ o K) 

Heat capacity 2.7910 6 2.7910 6 

J/m 3 / o K J/m 3 / o K 

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 model 

including rigid-viscoplastic workpiece, rigid tool, and 

the strain rate and temperature dependent flow stress. 

The model was verified by comparing predictions of 

cutting forces and chip morphology (metal flow) with 

carefully conducted experiments in the machining 

laboratory. 

Fig. 11: A comparison of measured and predicted cutting 

forces at different feed rates and cutting speeds 

354


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

355


problems such as, 

• Optimal machining parameters for a given 

material, heat treatment and part geometry 

• Increased material removal rates for minimizing 

machining times 

• Improved workpiece functional attributes such 

as surface integrity and precision 

• Design of cutting tool geometries and materials 

for increased tool lives and reduced tool changes. 

4. SOLIDIFICATION PROCESSING 

AND POROSITY CONTROL 

4.1 Die Casting of Engine Block: Application in 

44, 45 

Automotive Industry 

With the emphasis on light weight cars, automotive 

companies are increasingly using die cast engine blocks 

from high silicon aluminum alloys (Fig. 13). In these 

castings, the main cause of defect is leaker paths in 

certain critical areas of the castings due to 

microporosity. These leaker defects cause the cylinder 

block to fail the pressure leakage test and such castings 

have to be discarded as scrap. The aim of this study 

was to redesign the gate and optimization of the 

ingate parameters with a focus on minimum air 

entrapment for minimum gas porosity and better 

filling of thick sections for reduces shrinkage related 

defects. 

4.2 Location and Identification of Porosity 

Analysis of pressure test results on the die cast and 

machined engine blocks indicated that most of the 

leakage occurred from two locations shown in Fig. 13: 

Region 1 near the bearing area and Region 2 near the 

coolant entry area (the vent area for the die casting). 

Sections were cut from these locations in the cast 

dies, polished and examined. While Region 1 showed 

classical porosity linked to shrinkage due to thermal 

gradients, Region 2 showed the presence of pores 

which were not spherical, Fig. 14. 

The latter pores were analyzed using SEM techniques. 

It was found that while the composition on the outside 

regions of the pores represented the typical 

composition of the Al 380 die casting alloy, that in 

the inner regions showed a high presence of oxygen, 

Fig. 15. This is an indication of air being trappped 

during the die casting process (poor filling during 

metal injecttion). It was decided to focus on reducing 

or eliminating air or gas entrapment during metal 

injection by optimizing the the metal flow die runner 

system. 

4.3 Flow Optimization procedure 

The parameters used in this optimization study were 

gate velocity, fill time and flow angle for the fan 

and the tangent gates. This simulation study was based 

on CastView®, a software developed at The Ohio 

State University with support from NADCA (North 

American Die Casting Association). The design 

alternatives 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 the 

bearing area, Region 2 near the vent area. 

356


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

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

A Box-Behnken design array with 15 runs, inclusive 

of 3 center runs, was chosen for this three -level / 

three-factor study, Fig. 16. Simulations were 

performed in CastView for all the runs and the results 

were analyzed with a view for optimization the filling 

process. An appropriate response variable was chosen 

with the objective to obtain a proper fill in which the 

region closest to the vent fills last, and the adjoining 

areas fill immediately before this region, and so on. 

A regression model was built with the results of the 

analysis. The regression model was maximized using 

Microsoft Excel® software, in keeping with the 

objective of maximizing the response (the regions 

near the vents should fill last). The regression equation 

is 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 the 

gate velocity (m/s),C refers to the flow angle (degrees) 

The range of variation used for the parameters was 

as defined in the design array. It was found that the 

optimum values for maximum response correspond 

to the maximum value of the gate velocity, minimum 

value of the fill time and flow angle in the range of 

variation. A runner was designed for the best design 

alternative using standard NADCA guidelines. 

4.4 Comparison of the new design and existing 

design using FLOW3D 

A cavity filling simulation using the new gate design 

parameters was performed using the software package 

Flow3D (a finite difference software for fluid 

dynamics) and compared with simulations performed 

with existing gate designs 45 . For this simulation the 

best design alternative was chosen. Using design 

357


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

symmetry, a two-cylinder model was used for 

simulation as it reasonably represents the filling 

characteristics of the entire block since cross-flow 

between cylinders is very less. 

The results and comparisons of the simulations are 

shown in Fig. 17. In the simulation of the existing 

design, the runner system is included while in the 

simulation of the new design, a runner system has 

not been included. Consequently, in the new design 

the metal reaches the gate very fast, whereas in the 

existing design the metal reaches the gate only after 

0.1 sec. So the comparison plots have been made at 

the same times that have elapsed after the metal 

reached the ingate. The figures only show the regions 

that have been filled with metal. 

In all the three figures, we can see that in the case 

of the new design the filling is faster than the existing 

ingate design case. The bearing areas get filled much 

faster and hence there is more time for the thick 

sections to solidify and this could lead to reduced 

shrinkage defects in the region. The vent region and 

the adjoining areas also get filled at almost the same 

time and hence there is lesser chance of entrapped 

gas porosity in that region in the new design. From 

the above comparison it can be seen that the new 

ingate design combined with a larger ingate velocity 

favors better filling in the bearing and the vent regions. 

This will help in the reduction of entrapped gas 

porosity during filling and shrinkage porosity during 

the solidification stage. 

Fig. 17: The fill pattern in the new design (left) and the fill 

pattern in the original design (right) 45 


This study provided to the die casting industry a 

358


systematic analysis approach to the analysis of porosity 

and its elimination using computational approaches. 

5. FEM AND STATISTICAL METHODS 

5.1 Cracking in Cold Extruded Parts: Forging 

Industry 46-48 

While cold forging certain automotive drive 

components in industry, ‘End cracks’ were observed 

to occur randomly. As the name suggests, they are 

found on the front end of the extruded part. These 

cracks are radial and propagate in the longitudinal 

direction. They are often visible to the naked eye, 

showing up after the extrusion stage or during 

subsequent machining operation. An example of an 

end crack can be seen in Fig. 18(a). These cracks 

lead to significant economic losses as they increase 

the scrap volume and the requirement for inspection 

of each forged part once they are detected. Forging 

companies often resort to expensive processes like 

in-process annealing to reduce the probability of 

cracking. 

The center of an extruded product can develop cracks 

(variously known as center-burst, center-cracking, 

arrowhead-fracture, or chevron-cracking), as shown 

in Fig. 18(b). These cracks are attributed to a state 

of hydrostatic tensile stress (also called secondary 

tensile stresses) at the centerline of the deformation 

zone in the die. This situation is similar to the necked 

region in a uniaxial tensile-test specimen. The 

tendency for center cracking increases with increasing 

die angles and levels of impurities, and decreases 

with increasing extrusion ratio. 

The ‘Counter Shaft’ part (Fig. 18(a)) was the focus 

of this investigation. The billet material is 8620 steel. 

The shaft is manufactured by first shearing a billet 

from a rolled rod. Then three stages of extrusion 

(high ratios) which is followed by one stage of 

upsetting. In this particular family of parts, billets of 

larger diameter had a greater propensity for end 

cracking and the percentage of cracked parts reduced 

greatly by annealing the billets after the shearing 

process. Almost all cracks originated in the first 

extrusion operation. There was a greater tendency to 

crack when the burr formed in the shearing process 

was large, or if the sheared billet profile was rather 

uneven or oblique. Remedies tried in the past included 

sawing the billets instead of shearing, using smaller 

diameter billets in order to have reduced extrusion 

ratios and annealing and stress relieving. None of 

these remedies were able to deal with the cracking 

problem effectively. 

There are three types of issues that can be associated 

with this problem: 

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

cracking 

359


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 conditions 

which are difficult to control. Consequently, only 

the design issues were the focus of this investigation 

with the goal of developing guidelines for the design 

of forging-extrusion dies. 

A logical hypothesis was presumed to explain end 

cracking phenomenon during cold extrusion. The 

hypothesis can be stated as follows: (refer to Fig. 19) 

As the material is relieved out of the die land, due 

to elastic recovery, the surface of the extrudate tends 

to expand out while the center keeps flowing 

unimpeded. This differential expansion causes huge, 

tensile, circumferential stresses to develop close to 

the surface, while the center is still being compressed 

giving rise to a radial stress gradient. When the tensile 

hoop stresses close to the surface exceed a critical 

value, the crack initiates. This crack then propagated 

longitudinally, as more and more material is extruded. 

stress raiser causing fracture to occur. This explains 

the random nature of end cracks. 

A review of literature showed that many brittle 

materials are subject to circumferential (transverse) 

and longitudinal surface cracking during hydrostatic 

extrusion. This problem of extruding low-ductility 

materials was approached in an innovative way by 

some researchers at Battelle Columbus Labs 49 . They 

established that the cracks first developed in the rear 

section of the die land, immediately before the exit 

plane and that the surface cracking resulted from 

residual tensile stresses as the product left the die. 

The presence of a second small reduction (Fig. 20) 

prevents cracking by imposing an annular counterpressure 

in the extrudate as it exits the first portion 

of the die. This counters the axial tensile stresses 

arising from residual stresses, elastic bending and 

friction. Prevention of circumferential cracks upon 

exit from the second portion of the die is believed to 

be associated with the favorable permanent change in 

residual stresses in the workpiece caused by the second 

small reduction. 

Two FEM simulations 50 were carried out for the 

5.2 Finite element investigation 

Fig. 19: Elastic unloading of the material as it exits the die 49 

This fracture hypothesis was validated using Finite 

element Analysis of the extrusion process using 

DEFORM 2D v 5.1 50 . Simulations were carried out 

with elastic-plastic and rigid-plastic material models, 

the material having elastic-plastic properties showed 

significantly high residual circumferential stresses as 

compared to the material with rigid-plastic properties. 

While the stresses generated were just below the 

fracture stress of the material in the elastic-plastic 

case, the presence of random defects in the material 

such as seams, segregations, etc. may provide the 

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

Where: ‘ s – semi-die angles, L ‘s – Land 

lengths, R – Relief between stages, - Coefficient 

of friction, r ‘s – Radiuses 

360


‘Counter Shaft’ part. The first was the conventional 

die with a single reduction, while the second one was 

the new die design with double reduction. The total 

reduction 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 circumferential 

direction (Fig. 21 and Fig. 22) shows a significant 

reduction (above 50%) in the case with the double 

land (from 103.99 ksi to 45.5 ksi). As expected, this 

is due to the compressive stresses developed at the 

second reduction, which counteract the tensile stresses 

at the first stage. From the simulation results, we can 

conclude that the double reduction die is a good way 

of reducing the circumferential tensile stresses in the 

workpiece at the die exit. This helps in dealing with 

end cracks to a certain extent. 

On the other hand, the load requirements on the 

press are increased about 23% owing to the presence 

of the extra reduction. This might be one of the 

constraints in the design process. The other 

disadvantage of this design change is that it may lead 

to high, tensile axial stresses along the center of the 

extruded part. This might lead to ‘centerburst’ or 

‘chevron cracking’. 

5.3 Statistical Analysis 

It was noted that the decrease in tensile circumferential 

stresses (that cause end cracking) was accompanied 

by a corresponding increase in the axial stresses (that 

cause chevron cracking). Hence, there is a need to 

optimize the die design such that the stresses in the 

material at the die exit are kept at a minimum. 

The following factors are identified for further 

investigation (see Fig. 20): relief between stages (R, 

inches), die angle (a, degrees), land length at second 

stage (L, inches), % reduction at second stage, friction 

(m). The corner radii being very small have been 

neglected in this investigation. Using ‘Design of 

Experiments’ (DOE) 52 the above parameters were 

screened to see which ones were important for further 

investigation. A 2 52 design was chosen. This resulted 

in 8 simulation runs. Based on industry practices, the 

high and low values were established for each of the 

parameters. These values were decided. The 

circumferential stress ( q 

) at the die exit was the 

essential response. In addition, the axial stress ( a 

, 

which might lead to chevron cracking) was the 

secondary response. All the factors were found 

significant with respect to both these responses and 

hence were chosen for further investigation. 

Once the importance of various parameters was 

established, a final DOE was carried out for the 

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

361


objective of eliminating end cracking in the extruded 

shafts, it is necessary to contain the maximum 

circumferential stress ( 

) and the maximum axial 

stress ( z 

) below the fracture strength of the material 

in 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*a 2 ) – (1.39*d 2 ) + (496.06*e 2 ) + 

(7.5*a*d) + (381.23*a*e) + (90.22*d*e) 

Fig. 22: Circumferential stress at die exit for the optimal 

design (Max. value: 65.16Ksi, predicted value: 59Ksi) 

optimization of the design. The model selected was 

a 3-level, five factor DOE. Using a ‘fractional 

factorial’ design, the same experiment was conducted 

with a reasonable level of accuracy with 15 runs. 

The ranges for the parameters were same as the 

screening experiment, while the middle value was 

simply the average of the low and high levels (see 

Table 3). As in the screening experiment, the 

circumferential stress ( q 

) was the main response and 

the axial stress ( z 

) was a secondary response. 

Table 3 

LOW, 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 were 

obtained for circumferential stress and axial stress in 

terms of the design variables (factors). 

5.4 Optimization of the die design 

Using the regression equations and the values of the 

design parameters from common industry knowledge 

and practices, the following nonlinear minimization 

problem was formulated. To meet the preliminary 

Subject to: 

z 

= (79.97) + (256.16*a) - (13.78*b) + 

(31.04*c) - (1.81*d) + (91.79* e) - 

(225.72* a 2 ) + (0.664* b 2 ) + (0.08*d 2 ) - 

(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 (die 

angle) 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 following 

optimum solution (Table 4) to the problem was 

obtained: 

Table 4 

OPTIMAL VALUES OF THE DESIGN PARAMETERS 

Variable Parameter name Optimal value 

a * relief between stages 0.587 in 

b * die angle 5.146 o 

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 into 

DEFORM2D and was tested for consistency (Fig. 22). 

The predicted and observed values were very much 

in agreement, as shown in Table 5. The observed 

362


and the predicted values deviate by +10.44 % for 

and by -7.27 % for z 

. 

Table 5 

OPTIMAL VALUES OF THE STRESSES AND THEIR 

FACTORS OF SAFETY 

Variable Optimal Value Fracture Factor of 

From From stress(2) Safety 

Equation 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 required 

flexibility while choosing the values of the die design 

parameters, while maintaining the stresses (both axial 

and circumferential) well below their minimum. In 

Table 4, the lower limit is the smallest value that the 

parameter can take while holding all other parameters 

fixed and still satisfy the constraints. The upper limit 

is the greatest value. Table 6 shows the safe ranges 

for each parameter, determined by sensitivity analysis 

and rounded off. 

Table 6 

RANGES FOR THE DIE DESIGN PARAMETERS AND 

Parameter 

THEIR EFFECT ON THE STRESSES 

relief between stages 

die angle 

die land 

Safe range 

0.55 in – 0.75 in 

5 o – 8 o 

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 steel 

was constructed. These guidelines are meant to be 

used with Finite Element Analysis. When a simulation 

is conducted for 8620 steel, the fracture limits can be 

determined from the above figure. The area O-A-B- 

C is the safe operating zone. 

Various stress states were looked into at the different 

stages of extrusion. A comparison of the stress states 

was thus made between the single reduction die 

(original design) and double reduction die (optimal 

design). A ‘point tracking’ routine was undertaken 

using DEFORM2D. One typical point on the billet, 

in the area where stress is maximum, was selected 

and its stress profile was tracked for the entire 

extrusion process. This was done for both the single 

and double reduction die. 

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

363


It was found that both single and double reduction 

dies follow almost similar paths for circumferential 

stress, since the nature of the deformation is similar. 

Also the axial stress paths are almost similar for the 

first reduction and emergence from the first land. 

Since the percentage reduction is lesser at the first 

stage of the double reduction die as compared to the 

single reduction die, there are some tensile axial 

stresses at the center in the case of the former. 

Industrial trials with the new double reduction die 

design eliminated the cracks in the typical trial of 

10,000 parts. This validated the design predictions. 

7. CONCLUSIONS 

Advances in numerical techniques along with accurate 

modeling of material behavior have made it possible 

to analyze and optimize deformation and solidification 

processes for significant improvement in process 

quality and productivity. Recently, these techniques 

have been augmented by AI tools such as fuzzy 

reasoning and ANNs that enable incorporation of 

domain knowledge. In addition, SPC and robust 

design techniques have been integrated to reduce 

variability and to improve product properties. The 

collaborative industrial-governmental-academic 

research being conducted at the Manufacturing 

Research Group, The Ohio State University has 

resulted in significant cost reduction, and quality and 

productivity improvements for the participating 

industry. The cases presented in this paper are only 

a few examples of the application of these advanced 

theoretical techniques to the steel mills and the 

aerospace and automotive manufacturers (die casting 

and forging). The goal of this paper was to 

demonstrate the few successes of this collaborative 

effort. 

ACKNOWLEDGMENTS 

The support provided by the member companies 

(Timken, Inland steel and Chaparral steel) of the 

Consortium for the Advancement of Rolling 

Technology, by the Volvo Car Company, by the 

Sikorsky Aircraft Corporation, the Metaldyne 

Corporation and by the Dynamic Systems Incorporated 

(DSI) is gratefully acknowledged. The author also 

wishes to acknowledge the support from the 

Department of Energy and the UES, Inc; from SFTC, 

Columbus OH, for providing FEA software DE- 

FORM_2D TM ; and from TechSolve, Cincinnati OH 

for providing help with experiments for the machining 

research. The author finally expresses his appreciation 

to Praveen Pauskar, Jiang Hua, Shivakumar Kannan, 

Venkat Sankararaman, Ashish Pabalkar, Peeyush 

Mittal and Satish Kini, and the former and current 

research associates at The Ohio State University, for 

their hard work and efforts. 

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