ATEAS V1(1):: American Transactions on Engineering & Applied Sciences

American Transactions on
Engineering & Applied Sciences
IN THIS ISSUE
A Novel Finite Element Model for
Annulus Fibrosus Tissue Engineering
Using Homogenization Techniques
Relevance Vector Machines for
Earthquake Response Spectra
Influence of Carbon in Iron on
Characteristics of Surface Modification
by EDM in Liquid Nitrogen
Establishing empirical relations to
predict grain size and hardness of
pulsed current micro plasma arc
welded SS 304L sheets
Cyclic Elastoplastic Large
Displacement Analysis and Stability
Evaluation of Steel Tubular Braces
SAFARILAB: A Rugged and Reliable
Optical Imaging System
Characterization Set-up for Industrial
Environment
Volume 1 Issue 1
(January 2012)
ISSN 2229-1652
eISSN 2229-1660
http://TuEngr.com/ATEAS

International Editorial Board
Editor-in-Chief
Zhong Hu, PhD
Associate Professor, South Dakota State University,
USA
Executive Editor
Boonsap Witchayangkoon, PhD
Associate Professor, Thammasat University,
THAILAND
Associate Editors:
Associate Professor Dr. Ahmad Sanusi Hassan (Universiti Sains Malaysia )
Associate Prof. Dr.Vijay K. Goyal (University of Puerto Rico, Mayaguez)
Associate Professor Dr. Narin Watanakul (Thammasat University, Thailand )
Assistant Research Professor Dr.Apichai Tuanyok (Northern Arizona University, USA)
Associate Professor Dr. Kurt B. Wurm (New Mexico State University, USA )
Associate Prof. Dr. Jirarat Teeravaraprug (Thammasat University, Thailand)
Dr. H. Mustafa Palancıoğlu (Erciyes University, Turkey )
Editorial Research Board Members
Professor Dr. Nellore S. Venkataraman (University of Puerto Rico, Mayaguez USA)
Professor Dr. Marino Lupi (Università di Pisa, Italy)
Professor Dr.Martin Tajmar (Dresden University of Technology, German )
Professor Dr. Gianni Caligiana (University of Bologna, Italy )
Professor Dr. Paolo Bassi ( Universita' di Bologna, Italy )
Associate Prof. Dr. Jale Tezcan (Southern Illinois University Carbondale, USA)
Associate Prof. Dr. Burachat Chatveera (Thammasat University, Thailand)
Associate Prof. Dr. Pietro Croce (University of Pisa, Italy)
Associate Prof. Dr. Iraj H.P. Mamaghani (University of North Dakota, USA)
Associate Prof. Dr. Wanchai Pijitrojana (Thammasat University, Thailand)
Associate Prof. Dr. Nurak Grisadanurak (Thammasat University, Thailand )
Associate Prof.Dr. Montalee Sasananan (Thammasat University, Thailand )
Associate Prof. Dr. Gabriella Caroti (Università di Pisa, Italy)
Associate Prof. Dr. Arti Ahluwalia (Università di Pisa, Italy)
Assistant Prof. Dr. Malee Santikunaporn (Thammasat University, Thailand)
Assistant Prof. Dr. Xi Lin (Boston University, USA )
Assistant Prof. Dr.Jie Cheng (University of Hawaii at Hilo, USA)
Assistant Prof. Dr. Jeremiah Neubert (University of North Dakota, USA)
Assistant Prof. Dr. Didem Ozevin (University of Illinois at Chicago, USA)
Assistant Prof. Dr. Deepak Gupta (Southeast Missouri State University, USA)
Assistant Prof. Dr. Xingmao (Samuel) Ma (Southern Illinois University Carbondale, USA)
Assistant Prof. Dr. Aree Taylor (Thammasat University, Thailand)
Assistant.Prof. Dr.Wuthichai Wongthatsanekorn (Thammasat University, Thailand )
Assistant Prof. Dr. Rasim Guldiken (University of South Florida, USA)
Assistant Prof. Dr. Jaruek Teerawong (Khon Kaen University, Thailand)
Assistant Prof. Dr. Luis A Montejo Valencia (University of Puerto Rico at Mayaguez)
Assistant Prof. Dr. Ying Deng (University of South Dakota, USA)
Assistant Prof. Dr. Apiwat Muttamara (Thammasat University, Thailand)
Assistant Prof. Dr. Yang Deng (Montclair State University USA)
Assistant Prof. Dr. Polacco Giovanni (Università di PISA, Italy)
Dr. Monchai Pruekwilailert (Thammasat University, Thailand )
Dr. Piya Techateerawat (Thammasat University, Thailand )
Scientific and Technical Committee & Editorial Review Board on Engineering and Applied Sciences
Dr. Yong Li (Research Associate, University of Missouri-Kansas City, USA)
Dr. Ali H. Al-Jameel (University of Mosul, IRAQ)
Dr. MENG GUO (Research Scientist, University of Michigan, Ann Arbor)
Dr. Mohammad Hadi Dehghani Tafti (Tehran University of Medical Sciences)
2012 American Transactions on Engineering & Applied Sciences.

Contact & Office:
Associate Professor Dr. Zhong Hu (Editor-in-Chief), CEH 222, Box 2219 Mechanical
Engineering Department, College of Engineering, Center for Accelerated Applications at the Nanoscale and Photo-
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Zhong.Hu@sdstate.edu, Editor@TuEngr.com Postal Paid in USA.
ISSN 2229-1652 eISSN 2229-1660 http://tuengr.com/ATEAS
FEATURE PEER-REVIEWED ARTICLES for Vol.1 No.1 (January 2012)
A Novel Finite Element Model for Annulus Fibrosus Tissue
Engineering Using Homogenization Techniques
1
Relevance Vector Machines for Earthquake Response Spectra 25
Influence of Carbon in Iron on Characteristics of Surface
Modification by EDM in Liquid Nitrogen
41
Establishing empirical relations to predict grain size and
hardness of pulsed current micro plasma arc welded SS 304L
sheets
57
Cyclic Elastoplastic Large Displacement Analysis and Stability
Evaluation of Steel Tubular Braces
75
SAFARILAB: A Rugged and Reliable Optical Imaging System
Characterization Set-up for Industrial Environment
91

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American Transactions on Engineering
& Applied Sciences
A Novel Finite Element Model for Annulus
Fibrosus Tissue Engineering Using
Homogenization Techniques
Tyler S. Remund
a
, Trevor J. Layh
b
, Todd M. Rosenboom
b
,
Laura A. Koepsell
a
, Ying Deng
a*
, and Zhong Hu
b*
a
Department of Biomedical Engineering Faculty of Engineering, University of South Dakota, USA
b
Department of Mechanical Engineering Faculty of Engineering, South Dakota State University, USA
A R T I C L E I N F O A B S T RA C T
Article history:
Received September 06, 2011
Received in revised form -
Accepted September 24, 2011
Available online: September 25,
2011
Keywords:
Finite Element Method
Annulus Fibrosus
Tissue Engineering
Homogenization
In this work, a novel finite element model using the
mechanical homogenization techniques of the human annulus
fibrosus (AF) is proposed to accurately predict relevant moduli of
the AF lamella for tissue engineering application. A general
formulation for AF homogenization was laid out with appropriate
boundary conditions. The geometry of the fibre and matrix were
laid out in such a way as to properly mimic the native annulus
fibrosus tissue’s various, location-dependent geometrical and
histological states. The mechanical properties of the annulus
fibrosus calculated with this model were then compared with the
results obtained from the literature for native tissue.
Circumferential, axial, radial, and shear moduli were all in
agreement with the values found in literature. This study helps to
better understand the anisotropic nature of the annulus fibrosus
tissue, and possibly could be used to predict the structure-function
relationship of a tissue-engineered AF.
2012 American Transactions on Engineering and Applied Sciences.
2012 American Transactions on Engineering & Applied Sciences
*Corresponding authors (Y.Deng). Tel/Fax: +1-605-367-7775/+1-605-367-7836. E-mail
addresses: ying.deng@usd.edu. (Z.Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878.
E-mail address: Zhong.hu@sdstate.edu. 2012. American Transactions on Engineering
& Applied Sciences. Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660
Online Available at http://TUENGR.COM/ATEAS/V01/01-23.pdf
1

1. Introduction
The annulus fibrosus (AF) is an annular cartilage in the intervertebral disc (IVD) that aids in
supporting the structure of the spinal column. It experiences complex, multi-directional loads
during normal physiological functioning. To compensate for the complex loading experienced,
the AF exhibits anisotropic behavior, in which fibrous collagen bundles that are strong in tension,
run in various angles in an intersecting, crossing pattern which helps to absorb the loadings. (Wu
and Yao 1976) The layers of the AF are composed of fibrous collagen fibrils that are oriented in
such a way that the angles rotate from 28± degrees relative to the transverse axis of the spine in
the outer AF (OAF) to 44± degrees relative to the transverse axis of the spine in the inner AF
(IAF). (Hickey and Hukins 1980; Cassidy, Hiltner et al. 1989; Marchand and Ahmed 1990).
The approach that homogenization offers to deal with anisotropic materials includes
averaging the directionally-dependent mechanical properties in what is called a representative
volume elements (RVE). These RVE are averages of the directionally- and spatially-dependent
material properties. When summed over the volume of the material, they can be very useful in
describing the macroscopic mechanical properties of materials with complex microstructures.
(Bensoussan A 1978; Sanchez-Palencia E 1987; Jones RM 1999) Homogenization has been
applied to address some of the shortcomings of structural finite element analysis (FEA) models
that utilized truss and cable elements (Shirazi-Adl 1989; Shirazi-Adl 1994; Gilbertson, Goel et al.
1995; Goel, Monroe et al. 1995; Lu, Hutton et al. 1998; Lee, Kim et al. 2000; Natarajan,
Andersson et al. 2002) and fiber-reinforced strain energy models (Wu and Yao 1976; Klisch and
Lotz 1999; Eberlein R 2000; Elliott and Setton 2000; Elliott and Setton 2001) for modeling the
AF. Homogenization has also been used to describe biological tissues such as trabecular bone
(Hollister, Fyhrie et al. 1991), articular cartilage (Schwartz, Leo et al. 1994; Wu and Herzog
2002) and AF. (Yin and Elliott 2005).
The mechanical complexity of the AF has posed substantial problems for engineers
attempting to model the system. To date, the circumferential modulus and axial modulus have
been predicted accurately, but the predicted shear modulus has been consistently two orders of
magnitude high. An explanation proposed in a recent paper (Yin and Elliott 2005), which offered
a novel homogenization model for the AF, is that the high magnitude prediction for shear
2 Tyler S. Remund, Trevor J. Layh, Todd M. Rosenboom, L. A. Koepsell, Y. Deng, Z. Hu

modulus can be explained by the fact that the models assume the tissue to be firmly anchored in
surrounding tissue, whereas the experimentally measured tissue is removed from its surrounding
tissue. This removal of the sample from surrounding tissue releases the fibers near the edge,
which prevents a portion of the fiber stretch component from being included as a part of the
overall shear measurement.
The purpose of this paper was to establish a novel method for modeling the AF using FEA
and homogenization theory that predicts the circumferential-, axial-, and radial- modulus
accurately while also predicting a shear modulus that accurately represents that of the
experimentally measured tissue. A general formulation for annulus fibrosus lamellar
homogenization was laid out. Appropriate changes to the boundary conditions as well as the
geometry of the structural fibres was made to accommodate the measurements of the mechanical
properties under various annulus fibrosus volume fractions and orientations. The specific
changes in the three dimensional location and orientation of the cylindrical, crossing fibers within
the matrix was taken into account. And the mechanical properties of the human AF by modeling
were compared with the results obtained in the literatures for the native tissues.
2. Mathematical Model
The general homogenization formulation used here was applied to the AF before. (Yin and
Elliott 2005) In the homogenization approach volumetric averaging is used to arrive at the
general formulation. (Sanchez-Palencia 1987; Bendsoe 1995; Jones RM 1999) The
homogenization formula is created by averaging material properties for a material that is assumed
to be linear elastic over discrete, volumetric segments. The overall material is assumed to have
inhomogeneous properties throughout the entire volume. So, the average material properties can
be calculated by multiplying the inhomogeneous, localized material properties c by the
independent strain rates u, in independent strain states βα, , over the volume of the tissue Ω like
in Eq. (1).
∫Ω
Ω
Ω
= duuC lkji
βα
βα ,,,
1
(1)
3

βα ,C : overall average material properties
lkjic ,,, : non-homogeneous material properties
jiu , : independent strain rates
βα, : independent strain rates
Ω : volume
The stiffness tensor Eq. (2) rotates around a certain angle, α , in both the positive and
negative direction. This tensor thus rotates the average material properties to simulate the
direction of the AF collagenous fibers. This angle, α , is measured from the midline, θ , and it
changes with spatial location.
RCRC T
⋅=α
(2)
∞
C : average elasticity tensor for two lamellae
R: rotation tensor
The elasticity tensor of two, combined lamella Eq. (3) rotated at the same angle, α , in
opposite directions .
2
/
αα
α
−+
−+ +
=
CC
C (3)
There are four in-plane material properties: 11C , 22C , 12C , and 66C that are calculated for a
single lamella. They are arranged in matrix notation, like in Eq. (4).
C










=
66
2212
1211
00
0
0
C
CC
CC
(4)
And the values for 11C , 22C , 12C , and 66C can be calculated from the system of equations
shown in Eq. (5) using the height of the fiber portion of the segment ρ , the elastic modulus of
the fiber and matrix mf EE , respectively and the Poisson ratio of the fiber and matrix mf υυ ,
respectively:

( ) ( ) ( )( )
( ) ( )( ) fmfm
fmmf
m
m
f
ff
m
m
f
f
EE
EEEEEE
C 22
2
2
2
2
2
2211
111
1
1
1
11
1
1 νρνρ
νρρν
ν
νρ
ν
νρ
ν
ρ
ν
ρ
−−+−
−+
+
−
−
−
−
−
−
−
+
−
=
( )( )
( ) ( )( ) fmfm
fmmf
EE
EE
C 2212
111
1
νρνρ
νρρν
−−+−
−+
=
( ) ( )( ) fmfm
fm
EE
EE
C 2222
111 νρνρ −−+−
=
( ) ( )( ) fmfm
fm
EE
EE
C
νρνρ +−++
=
1112
1
66
(5)
ρ : height of the fiber
fE : elastic modulus of the fiber
mE : elastic modulus of the matrix
fv : Poisson ratio of the fiber
mv : Poisson ratio of the matrix
Taken together, this system of equations accurately modeled the AF in the existing model.
(Yin and Elliott 2005) It addressed many of the shortcomings of structural truss and cable
models and of strain energy models. However it did predict a shear modulus that was two orders
of magnitude higher than native tissue.
2.1 Model from the literature
The homogenization model for the AF created by Yin et al. accurately predicted most of the
important mechanical properties of the AF tissue. But it did not make accurate shear modulus
predictions. As a matter of fact, the predictions from this model were two orders of magnitude
higher than the measurements reported in the literature. In this section we will detail some
aspects of the published model that may contribute to the unnaturally high modulus prediction.
5

2.1.1 Fiber angle and fiber volume fraction
The first two important geometric considerations are the volumetric ratio of fiber to matrix
fiber volume fraction (FVF) within the RVE and the fiber angle. (Table 1) (Ohshima, Tsuji et al.
1989; Lu, Hutton et al. 1998) These ratios are used extensively in the calculations. Both the
FVF and the fiber angle vary by which lamina they are located in. But the finite element method
is a great tool for taking these variabilities into account. The original model used fiber angles in
the range of 15 to 45 degrees. It also used FVFs in the range of 0 to 0.3. These ranges were used
first in parametric studies in order to better understand how the fiber angle and FVF affect the
various relevant moduli. Also, beings fiber angle, and to a lesser extent FVF, can be determined
experimentally, the parametric studies helped in determining some of the more difficult to
elucidate material properties of the collagen fibers and the proteoglycan matrix.
2.1.2 Fiber configuration
The second important geometric consideration is the 3D arrangement of the fibers and matrix
within the composite RVE. In the original formulation, (Yin and Elliott 2005) they assumed the
two fiber populations to be within a single continuous material and not layered as in native tissue
structure. (Sanchez-Palencia 1987)
2.1.3 Boundary conditions
The final important consideration is the boundary conditions applied to the RVE. The
boundary condition for the tensile case can be seen in Figure 1. A similar boundary condition for
the tensile case was applied to the proposed model. But when they set the boundary conditions
for the shear case, they fixed the edges along both the θ - and z- axis when they applied a shear
along 1=z and 1=θ . (Sanchez-Palencia 1987) The proposed model has adopted a boundary
condition from (K. Sivaji Babu 2008), It constrains the rz-surface at 0=θ and applies a shear to
the rz surface at 1=θ . (K. Sivaji Babu 2008) This boundary condition can be visualized in
Figure 2. Taken together, these geometric considerations allow the proposed model of the AF
tissue’s mechanical behavior to be accurate.
2.2 Proposed model changes
Changes to the original model are proposed here. They include changes to the fiber angle
and FVF in order to bring them closer to the physiological range. Changes in the fiber
configuration were proposed in order to more closely mimic the native state of the tissue where

the crossing collagen fibers are separated by a section of proteoglycan matrix, whereas in the
original model they were welded together in the shape of an ‘X’. The final change made to the
original model was in the applied boundary conditions.
2.2.1 Fiber angle and fiber volume fraction
The ranges for this study were based loosely on the values used for the original study. In this
simulation graphs of circumferential-, axial-, and radial- modulus as well as shear modulus
against fiber volume fraction at fiber angles of 20, 25, 30, and 35 degrees were generated.
Graphs were also generated for axial- and circumferential- modulus as well as shear modulus
against varying fiber angle at fiber volume fractions of 0.05, 0.1, 0.15, 0.2, 0.25, and 0.3. The
angles of collagen in native tissue range from 24.5-36.3 degrees to the transverse plane with an
average of 29.6 degrees.
2.2.2 Fiber configuration
In this paper it is assumed that the fiber populations are layered and separated by matrix
material. The three dimensional geometric arrangement for this fiber and matrix composite is
shown in Figure 1 as a RVE along with the tensile case’s boundary conditions. The
corresponding RVE for the shear case is shown in Figure 2. With the material being a
composite, it is important to assign dimensions to repeating components within the RVE. The
width of the segment, which is denoted by c in Eq. (6) was set to be equal to 13 times the radius,
r, of the fiber when the number of fibers, n, within the RVE is 4. This means that the distance
between fibers is the equivalent of one radius. The length of b is dependent on the fiber angle α
and the length of a. Eq. (7) The length of a was derived from looking at the ratio of total fiber
volume to total segment volume. A number of new variables are introduced in the derivation of a
Eq. (8). So a can be derived from Eq. (9) by substitution of Eq. (10) and then rearranging.
rc ⋅= 13 (6)
( )αtan⋅= ab (7)
( )αρ
π
sin
4 2
⋅⋅
⋅
=
c
r
a (8)
7

Figure 1: Meshed 3D geometric representation of matrix and fiber orientation along with
coordinate system, dimensions, and tensile boundary conditions.

Figure 2: Meshed 3D geometric representation of composite RVE along with corresponding
axes, dimensions, and shear boundary conditions.
cba
rln
V
V f
RVE
fiber
⋅⋅
⋅⋅⋅
==
2
π
ρ (9)
( )α2
tan1+= al f (10)
After substituting, making use of a trigonometric identity, and rearranging, the simplified
formula for a, becomes clear.
So to equally space the four fibers along the c edge from each other and also the edge of the
matrix, the length d was derived as given by Eq. (11). It makes use of the idea that when there
9

are four fibers within the RVE, that there are five equal divisions of width.
r
rcn
d +
⋅⋅⋅
=
5
2
(11)
a : width of the representative volume element
b : height of the representative volume element
c : length of the representative volume element
d : distance between fibers
n : number of fibers in the representative volume element
r : radius of the fibers
α : angle between fibers.
So by putting the above equations into the prototype code, a master program code was
developed that is useful for predicting the various moduli at each variation of fiber angle and
FVF.
2.2.3 Boundary conditions
The original paper had fixed boundary conditions along two adjoining faces of the RVE and
applied shear on the two opposite faces of the RVE. In the proposed model one face has fixed
boundary conditions, and the opposite face has an applied shear. These changes taken together
make for a model that predicts all moduli, including the shear modulus, accurately.
3. Material Properties
It is also important to assign material properties to the parameters that remain constant
regardless of where they are measured throughout the AF. The elastic modulus and Poisson ratio
for the collagen fibers and proteoglycan matrix can be assigned specific values. For modeling the
varying conditions of the AF tissue, laminae, and IVD, the parameters were chosen based on the
literature of past numerical models of the AF, and in some cases, direct measurements of the

tissues. An elastic modulus of 500 MPa and a Poisson’s Ratio of 0.35 were adopted for the
collagen fibers (Goel, Monroe et al. 1995; Lu, Hutton et al. 1998), while an elastic modulus of
0.8 Mpa (Lee, Kim et al. 2000; Elliott and Setton 2001) and a Poisson’s Ratio of 0.45 (Shirazi-
Adl, Shrivastava et al. 1984; Goel, Monroe et al. 1995; Tohgo and Kawaguchi 2005) were
assigned to the proteoglycan matrix. Fiber volume fractions and fiber angles were varied over
ranges found in previous homogenization.
4. Results
The first input parameter from the lamina that is varied in order to investigate the effect on
the various moduli is the FVF. The FVF is varied from 0.05 to 0.3, which are normal
physiological ranges. (Table 1) Table 1 gives estimates for the cross-sectional area of the AF,
FVF of the AF, and fiber angle. Each are estimated for the corresponding lamella. Of course
these parameters are variable throughout the AF. But this list was compiled for the original
model, so it was used here for ease of comparison. There are also more than six lamellar layers
in the AF, but six is a reasonable approximation.
Table 1: Annulus fibrosus cross-sectional area for each of the lamina layers, collagen fiber
volume fraction for each of the lamina layers, and fiber orientation angle as reported in the
literatures. These values were inserted into the proposed formulation.
Lamina Layer Inner 2nd 3rd 4th 5th Outer References
Annulus fibrosus
cross sectional area
0.06 0.11 0.163 0.22 0.2662 0.195 (Lu, Hutton et al.
1998)
Collagen fiber
volume fraction
0.05 0.09 0.13 0.17 0.2 0.23 (Yin and Elliott
2005)
Fiber angle Annulus Fiber orientation average: 29.6 (range 24.5-36.3)
(Lu, Hutton et al.
1998)
11

Figure 3 looks at how the circumferential modulus varies with varying FVF and fiber angle.
At a fiber angle of 20 degrees the circumferential modulus varies from 7 Mpa at a FVF of 0.05 to
26 Mpa at a FVF of 0.3. At a fiber angle of 35 degrees the circumferential modulus varies from 2
Mpa at a FVF of 0.05 to 17 Mpa at a FVF of 0.3.
Figure 3: Circumferential modulus vs. fiber volume fraction at various fiber angles.
Figure 4 takes a look at how the axial modulus varies with FVF and fiber angle. The axial
modulus at a fiber angle of 20 degrees varies from 1 Mpa at a FVF of 0.05 to 4 Mpa at a FVF of
0.3. It also varies from 1 Mpa at a FVF of 0.05 to 9 Mpa at a FVF of 0.3 when the fiber angle is
35 degrees.

Figure 4: Axial modulus vs. fiber volume fraction at various fiber angles.
Figure 5: Shear modulus vs. fiber volume fraction at various fiber angles.
13

In Figure 5 the shear modulus is evaluated against fiber volume fraction at various fiber
angles. The shear modulus, at a fiber angle of 20 degrees, was 0.1 Mpa at a FVF of 0.05 and was
0.6 Mpa at a FVF of 0.3. The shear modulus, at a fiber angle of 35 degrees, was 0.3 Mpa at a
FVF of 0.05 and was 1.2 Mpa at a FVF of 0.3.
Figure 6 shows that the radial modulus seemed to depend very little on fiber angle. But it
also shows that radial modulus increases linearly with increasing FVF from 0 Mpa at a FVF of
0.05 to 1.6 Mpa at a FVF of 0.3.
Figure 6: Radial modulus vs. fiber volume fraction at various fiber angles.
The next input parameter from the lamina that is varied in order to investigate the effect on
the various moduli is the fiber angle. The physiologically-relevant range of fiber angles is
roughly 20 to 35 degrees (Table 1).
In Figure 7 the circumferential modulus at a FVF of 0.05 varies from 7 Mpa at a fiber angle
of 20 degrees to 2 Mpa at a fiber angle of 35 degrees, and at a FVF of 0.3 it varies from 25 Mpa
at a fiber angle of 20 degrees to 16 Mpa at a fiber angle of 35 degrees.

Figure 7: Circumferential modulus vs. fiber angle at various fiber volume fractions.
Figure 8: Axial modulus vs. fiber angle at various fiber volume fractions.
In Figure 8 the axial modulus at a FVF of 0.05 is 1 Mpa, and at a FVF of 0.3 it varies from
15

3.5 Mpa at a fiber angle of 20 degrees to 9 Mpa at a fiber angle of 35 degrees.
In Figure 9 the shear modulus at a FVF of 0.05 varies from 0.6 Mpa at a fiber angle of 20
degrees to 1.2 Mpa at a fiber angle of 35 degrees, and at a FVF of 0.3 it varies from 0.1 Mpa at a
fiber angle of 20 degrees to 0.2 Mpa at a fiber angle of 35 degrees.
Figure 9: Shear modulus vs. fiber angle at various fiber volume fractions.
Table 2: Values predicted by the model in both range form and real case calculations as
compared to the corresponding values of circumferential-, axial-, radial-, and shear- modulus
measured experimentally as found in the literature.
Modulus (Mpa)
Modeling Ranges
Fα[20-30] FVF
[0.05-0.30]
Real
Case
Experimental
Circumferential
Modulus
1.92≤E≤25.35 7.09
18±14
(Elliott and Setton 2001)
Axial Modulus 0.91≤E≤9.09 2.12
0.7±0.8
(Acaroglu, Iatridis et al. 1995)
(Ebara, Iatridis et al. 1996)
(Elliott and Setton 2001)
Radial Modulus 1.10≤E≤1.57 1.34
Shear Modulus 0.08≤G≤1.20 0.16
0.1
(Iatridis, Kumar et al. 1999)

The changes to the moduli are mostly linear. But while the axial- and shear- moduli (Figures
8-9) increase with increasing fiber angle, the circumferential modulus (Figure 7) decreases with
increasing fiber angle (Table 2).
While modeling ranges allow us to evaluate the effect of changing the input parameters such
as fiber angle and fiber volume fraction on the various mechanical characteristics of the tissue,
they don’t allow us to compare our model to the real case. Table 2 shows the ranges of the
moduli predicted by the model accompanied by the modulus predicted when the input parameters
used were what was assumed to be found in the human body. These values were then compared
to experimentally measured values found in literature.
5. Discussion
Here comparisons between the proposed model and existing homogenization model, as well
as the experimentally measured data from the literature, will be made. It is worth repeating that
in the 3D homogenization models, the fibres of the AF are modelled as truss or cable elements
that are strong in tension but not capable of resisting compression or bending moment. This
holds true for both the proposed as well as the existing homogenization model. Also, the surfaces
of the fiber and matrix that come into contact with each other are ‘glued’ as if the surfaces that
those two features share are actually one in the same. So the interface is a blend and there is no
slippage between the components at their respective interfaces.
An explanation would be in order for how the ‘real case’ moduli (Table 2) were calculated.
The fiber angle in the native tissue varies not only from lamella-to-lamella, but also within each
lamella. So an average fiber angle of 29.6 degrees was taken from the literature (Lu, Hutton et al.
1998). Fiber volume fraction is also variable, so a weighted FVF was used. To arrive at this
weighted FVF, an approximate FVF from each lamella was considered (Yin and Elliott 2005)
along with the cross sectional area of the corresponding lamella (Lu, Hutton et al. 1998). Using
these parameters, calculations were made for the moduli for each of the lamella. Then the moduli
were weighted based on the cross-sectional areas (Table 1) of the various lamellas relative to the
overall cross sectional area. Once the weighting factors were multiplied by the modulus for that
specific lamella, the various weighted moduli were summed to come to an actual modulus.
17

The existing model has a circumferential modulus in the 11 MPa range, an axial modulus of
around 2 MPa, and a shear modulus of around 18 MPa. Conversely, the proposed model had a
circumferential modulus of about 7 MPa, an axial modulus of about 2 MPa, and a shear modulus
of around 0.5 MPa. The experimentally measured values for these parameters are a
circumferential modulus in the range of 4-32 MPa, an axial modulus in the range of 0.1-1.5 MPa,
and a shear modulus of 0.1 MPa. (Table 2).
While there is agreement between the various models and the experimentally-measured
values from literature when it comes to tensile moduli, the models uniformly disagree with the
experimentally measured data from the literature when it comes to the shear modulus. The shear
modulus is over two orders of magnitude higher in the models than in the experimentally
measured data from the literature. The author suggested that this is because the tissue has to be
removed from its surroundings to be measured experimentally. (Yin and Elliott 2005) This frees
up the ends of the fibers so there is fiber sliding but not fiber stretching contributing to overall
shear measurements. Whereas the nature of the models can have more realistic in vivo boundary
conditions, so the tissue can experience both fiber stretch and fiber sliding in its shear
measurement. Conversely, the proposed model will more accurately emulate the former.
In this study, a homogenization model of the AF was revised to address the discrepancy
between the shear modulus prediction in the previously proposed model and the experimental
data of human AF tissue. The original model had a shear modulus two orders of magnitude
higher than that of the experimental values for native AF tissue. It was suggested that the shear
was lower in the experimental values, because the pieces of AF tissue were removed from their
native surroundings. This causes the fibers of the tissue near the edges to not be anchored into
the surrounding tissue. So the stretch of the tissue’s fibers may not have been contributing to
shear measurements. Here is suggested a model that gives accurate accounts of the shear
modulus in the AF tissue while not sacrificing modulus predictions in the circumferential-, axial-,
and radial-directions.
Several significant changes have been made to the reported model (Yin and Elliott 2005) to
address the discrepancy between the shear modulus in the model and that experimentally
measured in the native tissue. The first change made to the model was the arrangement of the

fibers and matrix within the RVE. In both this model and the original, there are four fibers. In
the original model there are two fibers on each opposing face. The two crossing fibers are in the
same plane, so they are in effect welded together. One of the changes made to this model is in
the geometrical layout of the fibers. The alternating fibers are separated in space and by matrix
material. This separation of the fibers allows them to slide against each other. Once the
arrangement of the fibers and the matrix were changed, the shear modulus prediction was
decreased. But it had decreased to a level much smaller than that of the native tissue value. The
value the model had predicted was actually 12
10−
MPa. This is much, much smaller than the
value tested in native tissue of roughly 0.1 MPa. So a literature search was performed to try to
find alternative approaches to improving shear predictions in homogenization models. The paper
that was found called for changing the boundary conditions. In the original model, two adjoining
sides of the RVE are constrained, and the opposing two sides of the RVE have the shear loadings
applied. This model has one side constrained at a time. The opposing side of the RVE has the
shear loading applied. This has brought the shear modulus prediction much closer to that tested
in the native AF tissue. And while the original model is likely more accurate for 3D predictions
as the tissue is in the IVD in vivo, if the aim is to develop a model that more accurately predicts
the mechanical properties of a resected piece of AF tissue as is measured in the literature, then
boundary conditions used in the proposed model are more applicable. This is because the
boundary conditions in the proposed model allow for the fibres to slide more freely, avoiding
incorporating fiber stretch, and resulting in significantly lower shear measurements.
This model is important in understanding the mechanics of the AF, especially when tissue
samples are resected from the greater IVD. It can be useful for better understanding disc
degeneration and for improving approaches to designing functional tissue engineered constructs.
It can help in understanding disc degeneration as the process is usually characterized by a
degradation of the proteoglycan matrix. Through the alteration of the matrix, disc degradation
can be modeled accurately. Also, more appropriate benchmarks for the design of functional
tissue engineered constructs can be set through the better understanding of the interaction of the
AF subcomponents that this model provides.
19

It should be noted that this model, like those proposed in the past, does not take interlamellar
interactions into account. To this point, it has not been determined if the interlamellar
interactions and interweaving, that have been observed in the literature, are of mechanical
significance.
6. Conclusion
In summary, this study established a novel approach to an existing homogenization model. It
more closely models the anisotropic AF tissue’s in-plane shear modulus as if it were excised
from the IVD. It did this while still making accurate predictions of circumferential-, axial-, and
radial- moduli. The lower shear stress predictions were more in line with experimental
measurements than past models. The model also elucidates the relationship between FVF, fiber
angle, and composite mechanical properties. The proposed model will also help to better
understand the structure-function relationship for future work with disc degeneration and
functional tissue engineering.
7. Acknowledgements
This research was partially supported by the joint Biomedical Engineering (BME) Program
between the University of South Dakota and the South Dakota School of Mines and Technology.
The authors would also acknowledge the South Dakota Board of Regents Competitive Research
Grant Award (No. SDBOR/USD 2011-10-07) for the financial support.
8. References
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Tissue Res 23(1): 75-88.
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fibrosus." Spine 21(4): 452-461.
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enhanced finite element analyses of intact lumbar bodies." Computational Methods in
Biomechanics and Biomedical Engineering: 1-20.
Elliott, D. M. and L. A. Setton (2000). "A linear material model for fiber-induced anisotropy of
the anulus fibrosus." J Biomech Eng 122(2): 173-179.
Elliott, D. M. and L. A. Setton (2001). "Anisotropic and inhomogeneous tensile behavior of the
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research." Crit Rev Biomed Eng 23(5-6): 411-473.
Goel, V. K., B. T. Monroe, et al. (1995). "Interlaminar shear stresses and laminae separation in a
disc. Finite element analysis of the L3-L4 motion segment subjected to axial compressive
loads." Spine (Phila Pa 1976) 20(6): 689-698.
Hickey, D. S. and D. W. Hukins (1980). "X-ray diffraction studies of the arrangement of
collagenous fibres in human fetal intervertebral disc." J Anat 131(Pt 1): 81-90.
Hollister, S. J., D. P. Fyhrie, et al. (1991). "Application of homogenization theory to the study of
trabecular bone mechanics." J Biomech 24(9): 825-839.
Iatridis, J. C., S. Kumar, et al. (1999). "Shear mechanical properties of human lumbar annulus
fibrosus." J Orthop Res 17(5): 732-737.
Jones RM (1999). Mechanics of Composite Materials. London, England, Taylor and Francis.
K. Sivaji Babu, K. M. R., V. Rama Chandra Raju, V. Bala Krishna Murthy, and MSR Niranjan
Kumar (2008). "Prediction of Shear Moduli of Hybrid FRP Composite with Fiber-Matrix
Interface Debond." International Journal of Mechanics and Solids 3(2): 147-156.
Klisch, S. M. and J. C. Lotz (1999). "Application of a fiber-reinforced continuum theory to
multiple deformations of the annulus fibrosus." J Biomech 32(10): 1027-1036.
Lee, C. K., Y. E. Kim, et al. (2000). "Impact response of the intervertebral disc in a finite-element
model." Spine (Phila Pa 1976) 25(19): 2431-2439.
Lu, Y. M., W. C. Hutton, et al. (1998). "The effect of fluid loss on the viscoelastic behavior of the
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lumbar intervertebral disc in compression." J Biomech Eng 120(1): 48-54.
Marchand, F. and A. M. Ahmed (1990). "Investigation of the laminate structure of lumbar disc
anulus fibrosus." Spine (Phila Pa 1976) 15(5): 402-410.
Natarajan, R. N., G. B. Andersson, et al. (2002). "Effect of annular incision type on the change in
biomechanical properties in a herniated lumbar intervertebral disc." J Biomech Eng
124(2): 229-236.
Ohshima, H., H. Tsuji, et al. (1989). "Water diffusion pathway, swelling pressure, and
biomechanical properties of the intervertebral disc during compression load." Spine (Phila
Pa 1976) 14(11): 1234-1244.
Sanchez-Palencia E, Z. A. (1987). Homogenization Techniques for Composite Media. Verlag,
Berlin, Springer.
Sanchez-Palencia, E. Z. A. (1987). Homogenization techniques for composite media. Berlin,
Springer Verlag.
Schwartz, M. H., P. H. Leo, et al. (1994). "A microstructural model for the elastic response of
articular cartilage." J Biomech 27(7): 865-873.
Shirazi-Adl, A. (1989). "On the fibre composite material models of disc annulus--comparison of
predicted stresses." J Biomech 22(4): 357-365.
Shirazi-Adl, A. (1994). "Nonlinear stress analysis of the whole lumbar spine in torsion--
mechanics of facet articulation." J Biomech 27(3): 289-299.
Shirazi-Adl, S. A., S. C. Shrivastava, et al. (1984). "Stress analysis of the lumbar disc-body unit
in compression. A three-dimensional nonlinear finite element study." Spine (Phila Pa
1976) 9(2): 120-134.
Tohgo, K. and T. Kawaguchi (2005). "Influence of material composition on mechanical
properties and fracture behavior of ceramic-metal composites." Advances in Fracture and
Strength, Pts 1- 4 297-300: 1516-1521.
Wu, H. C. and R. F. Yao (1976). "Mechanical behavior of the human annulus fibrosus." J
Biomech 9(1): 1-7.
Wu, J. Z. and W. Herzog (2002). "Elastic anisotropy of articular cartilage is associated with the
microstructures of collagen fibers and chondrocytes." Journal of Biomechanics 35(7):
931-942.
Yin, L. Z. and D. M. Elliott (2005). "A homogenization model of the annulus fibrosus." Journal
of Biomechanics 38(8): 1674-1684.

Tyler S. Remund is a PhD candidate in the Biomedical Engineering Department at the
University of South Dakota. He holds a BS in Mechanical Engineering from South Dakota State
University. He is interested in tissue engineering of the annulus fibrosus.
Trevor J. Layh holds a BS in Mechanical Engineering from South Dakota State University. After
graduation he was accepted into the Department of Defense SMART Scholarship for Service
Program in August 2010, Trevor is now employed by the Naval Surface Warfare Center
Dahlgren Division in Dahlgren, VA as a Test Engineer.
Todd M. Rosenboom holds a BS in Mechanical Engineering from South Dakota State
University. He currently works as an application engineer for Malloy Electric in Sioux Falls,
SD.
Laura A. Koepsell holds a PhD in Biomedical Engineering and a BS in Chemistry, both from the
University of South Dakota. She is a Postdoctoral Research Associate at the University of
Nebraska Medical Center Department of Orthopedics and Nano-Biotechnology. She is
interested in cellular adhesion, growth, and differentiation of mesenchymal stem cells on
titanium dioxide nanocrystalline surfaces. She is trying to better understand any inflammatory
responses evoked by these surfaces and to evaluate the expression patterns and levels of
adhesion and extracellular matrix-related molecules present (particularly fibronectin).
Dr. Ying Deng received her Ph.D. from Huazhong University of Science and Technology in 2001.
She then completed a post-doctoral fellowship at Tsinghua University and a second post-
doctoral fellowship at Rice University. In 2008, Dr. Deng joined the faculty of the University of
South Dakota at Sioux Falls where she is currently assistant Professor of Biomedical
Engineering. She has authored over 15 scientific publications in the biomedical engineering area.
Dr. Zhong Hu is an Associate Professor of Mechanical Engineering at South Dakota State
University, Brookings, South Dakota, USA. He has about 70 publications in the journals and
conferences in the areas of Nanotechnology and nanoscale modeling by quantum
mechanical/molecular dynamics (QM/MD); Development of renewable energy (including
photovoltaics, wind energy and energy storage material); Mechanical strength evaluation and
failure prediction by finite element analysis (FEA) and nondestructive engineering (NDE);
Design and optimization of advanced materials (such as biomaterials, carbon nanotube, polymer
and composites). He has been worked on many projects funded by DoD, NSF RII/EPSCoR,
NSF/IGERT, NASA EPSCoR, etc.
Peer Review: This article has been internationally peer-reviewed and accepted for publication
according to the guidelines given at the journal’s website.
23

Relevance Vector Machines for Earthquake
Response Spectra
Jale Tezcan
a*
, Qiang Cheng
b
a
Department of Civil and Environmental Engineering, Southern Illinois University Carbondale,
Carbondale, IL 62901, USA
b
Department of Computer Science, Southern Illinois University Carbondale, Carbondale, IL 62901, USA
Article history:
Received 23 August 2011
Received in revised form
23 September 2011
Accepted 26 September 2011
Available online
26 September 2011
Keywords:
Response spectrum
Ground motion
Supervised learning
Bayesian regression
Relevance Vector Machines
This study uses Relevance Vector Machine (RVM)
regression to develop a probabilistic model for the average horizontal
component of 5%-damped earthquake response spectra. Unlike
conventional models, the proposed approach does not require a
functional form, and constructs the model based on a set predictive
variables and a set of representative ground motion records. The
RVM uses Bayesian inference to determine the confidence intervals,
instead of estimating them from the mean squared errors on the
training set. An example application using three predictive
variables (magnitude, distance and fault mechanism) is presented for
sites with shear wave velocities ranging from 450 m/s to 900 m/s.
The predictions from the proposed model are compared to an existing
parametric model. The results demonstrate the validity of the
proposed model, and suggest that it can be used as an alternative to
the conventional ground motion models. Future studies will
investigate the effect of additional predictive variables on the
predictive performance of the model.
2011 American Transactions on Engineering & Applied Sciences.2012 American Transactions on Engineering & Applied Sciences
*Corresponding author ( J. Tezcan). Tel/Fax: +001-618-4536125. E-mail address:
jale@siu.edu. 2012. American Transactions on Engineering & Applied Sciences.
Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660. Online Available at
http://TUENGR.COM/ATEAS/V01/25-39.pdf
25

1. Introduction
Reliable prediction of ground motions from future earthquakes is one of the primary
challenges in seismic hazard assessment. Conventional ground motion models are based on
parametric regression, which requires a fixed functional form for the predictive model. Because the
mechanisms governing ground motion processes are not fully understood, identification of the
mathematical form of the underlying function is a challenge. Once a functional form is selected,
the model is fit to the data and the model coefficients minimizing the mean squared errors
between the model and the data are determined. This approach, when the selected mathematical
form does not accurately represent the actual input-output relationship, is susceptible to
overfitting. Indeed, using a sufficiently complex model, one can achieve a perfect fit to the
training data, regardless of the selected mathematical form. However, a perfect fit to the
training data does not indicate the predictive performance of the model for new data.
Kernel regression offers a convenient way to perform regression without a fixed parametric
form, or any knowledge of the underlying probability distribution. A special form of kernel
regression, called the Support Vector Regression (SVR) (Drucker et al., 1997) is characterized by
its compact representation and its high generalization performance. In SVR, the training data is
first transformed into a high dimensional kernel space, and linear regression is performed on the
transformed data. The resulting model is a linear combination of nonlinear kernel functions
evaluated at a subset of the training input. Combination weights are determined by minimizing a
penalized residual function. The SVR has proved successful in many studies since its introduction
in 1997. The effectiveness of SVR in ground motion modeling has been recently demonstrated
(Tezcan and Cheng, 2011), (Tezcan et al., 2010). A well-known weakness of the SVR is the lack
of probabilistic outputs. Although the confidence intervals can be constructed using the
mean-squared errors, similar to the approach used in conventional ground motion models, the
posterior probabilities, which produce the most reliable estimate of prediction intervals, are not
given. The lack of probabilistic outputs in the SVR formulation has motivated the development of
a new kernel regression model called Relevance Vector Machine (RVM) (Tipping, 2000) which
operates in a Bayesian framework.
To overcome the limitations of parametric regression while obtaining probabilistic
26 Jale Tezcan and Qiang Cheng

predictions, this paper proposes a new ground motion model based on the RVM regression.
Unlike standard ground motion models, which make point estimates of the optimal value of the
weights by minimizing the fitting error, the RVM model treats the model coefficients as random
variables with independent variances and attempts to find the model that maximizes the likelihood
of the observations. This approach offers two main advantages over the conventional ground
motion models. First, the prediction uncertainty is explicitly determined using Bayesian
inference, as opposed to being estimated from the mean squared errors. Second, the complexity of
the RVM model is controlled by assigning suitable prior distributions over the model coefficients,
which reduces the overfit susceptibility of the model.
The rest of the paper is organized as follows. In Section 2, the RVM regression algorithm is
described. Section 3 is devoted to the construction of ground motion model. Starting with the
description of the ground motion data and the predictive and target variables, the training results
are presented, and the prediction procedure for new data is described. Section 4 demonstrates
computational results and compares the RVM predictions to an existing empirical parametric
model. Section 5 concludes the paper by presenting the main conclusions of this study, and
discusses the advantages and limitations of the proposed method.
2. The RVM Regression Algorithm
Given a set of input vectors 𝑥𝑖, 𝑖 = 1: 𝑁 and corresponding real-valued targets 𝑡𝑖 , the
regression task is to estimate the underlying input-output relationship. Using kernel representation
(Smola and Schölkopf, 2004), the regression function can be written as a linear combination of a
set of nonlinear kernel functions:
𝑓(𝑥) = � 𝑤𝑖 𝐾(𝑥, 𝑥𝑖) + 𝑤0
𝑁
𝑖=1
(1)
where 𝑤𝑖, 𝑖 = 1 … 𝑁 are the combination weights and 𝑤0 is the bias term.
27

This study uses the radial basis function (RBF) kernel:
𝐾(𝑥𝑖, 𝑥𝑗), = 𝑒−𝛾�𝑥 𝑖−𝑥 𝑗�
2
, 𝛾 > 0 (2)
where 𝛾 is the width parameter controlling the trade-off between model accuracy and
complexity. In this study, the width parameter has been determined using cross-validation.
Assuming independent noise samples from a zero-mean Gaussian distribution,
i.e., 𝑛𝑖~𝒩(0, 𝜎 𝑛
2), the target values can be written as:
𝑡𝑖 = 𝑓(𝑥𝑖) + 𝑛𝑖 𝑖 = 1, … , 𝑁. (3)
Recast in matrix from, Equation (3) becomes:
𝑡 = Φw + 𝑛, (4)
where 𝑡 = (𝑡1, … , 𝑡 𝑁) 𝑇
, 𝑤 = (𝑤0, … , 𝑤 𝑁) 𝑇
, and Φ is an 𝑁 × 𝑁 + 1 basis matrix with 𝛷𝑖1 = 1
and 𝛷𝑖𝑗 = 𝐾�𝑥𝑖, 𝑥𝑗−1�. The likelihood of the entire set, assuming independent observations is
given by:
𝑝(𝑡|𝑤, 𝜎 𝑛
2) = (2𝜋𝜎 𝑛
2)−
𝑁
2 𝑒
−
1
2𝜎 𝑛
2 ‖𝑡−𝛷𝜇‖2
. (5)
where 𝜇 = (𝜇0, … , 𝜇 𝑁) 𝑇
is the vector containing the mean values of the combination weights.
To control the complexity of the model, a zero-mean Gaussian prior is used where each weight is
assigned a different variance (MacKay, 1992):
𝑝(𝑤|𝛼) = � 𝒩(0, 1/𝛼𝑖).
𝑁
𝑖=0
(6)

In Eq. (6), 𝛼 = (𝛼0, … , 𝛼 𝑁) where 1/𝛼𝑖 is the variance of 𝑤𝑖. The posterior distribution
of the weights is obtained as:
𝑝(𝑤|𝑡, 𝛼, 𝜎 𝑛
2) = (2𝜋)−
𝑁+1
2 |𝐶|−
1
2 𝑒−
1
2
(𝑤−𝜇) 𝑇 𝐶−1(𝑤−𝜇)
. (7)
where the mean vector 𝜇 and covariance matrix 𝐶 are:
𝜇 = 𝜎 𝑛
−2
𝐶 𝛷 𝑇
𝑡 (8)
𝐶 = [𝜎 𝑛
−2
𝛷 𝑇
𝛷 + 𝐴 ]−1 (9)
with
𝐴 = �
𝛼0 … … 0
: 𝛼1
⋮ ⋱ ⋮
0 … ⋯ 𝛼 𝑁
� . (10)
The marginal likelihood of the dataset can be determined by integrating out the weights (MacKay,
1992) as follows:
𝑝(𝑡|𝛼, 𝜎 𝑛
2 ) = (2𝜋)−
𝑁
2 |𝐻|−
1
2 𝑒−
1
2
𝑡 𝑇 𝐻−1 𝑡 (11)
where 𝐻 = 𝜎 𝑛
2
𝐼 𝑁 + 𝛷𝐴−1
𝛷 𝑇
and 𝐼 𝑁 is the identity matrix of size 𝑁. Ideal Bayesian inference
requires defining prior distributions over 𝛼 and 𝜎 𝑛
2
, followed by marginalization. This process,
however, will not result in a closed form solution. Instead, the 𝛼𝑖 and 𝜎 𝑛
2
values maximizing
Eq. (11) can be found iteratively as follows (MacKay, 1992):
29

(𝛼𝑖) 𝑛𝑒𝑤 =
1 − 𝛼𝑖 𝐶𝑖𝑖
𝜇𝑖
2 (12)
(𝜎 𝑛
2) 𝑛𝑒𝑤 =
‖𝑡 − 𝛷𝜇‖2
𝑁 − ∑ (1 − 𝛼𝑖 𝐶𝑖𝑖)
. (13)
Because the nominator in Eq.(12) is a positive number with a maximum value of 1, an 𝛼𝑖
value tending to infinity implies that the posterior distribution of 𝑤𝑖 is infinitely peaked at zero,
i.e. 𝑤𝑖 = 0. As a consequence, the corresponding kernel function can be removed from the
model. The procedure for determining the weights and the noise variance can be summarized as
follows:
1) Select a width parameter of the kernel function and form the basis matrix Φ.
2) Initialize 𝛼 = (𝛼0, … , 𝛼 𝑁) and 𝜎 𝑛
2
.
3) Compute matrix 𝐴 using Eq.(10).
4) Compute the covariance matrix 𝐶 using Eq.(9).
5) Compute the mean vector 𝜇 using Eq.(8).
6) Update 𝛼 and 𝜎 𝑛
2
using Eq.(12) and Eq.(13).
7) If 𝛼𝑖 → ∞, set 𝑤𝑖 = 0 and remove the corresponding column in Φ.
8) Go back to step 3 until convergence.
9) Set the remaining weights equal to 𝜇 .
The training input points corresponding to the remaining nonzero weights are called the
“relevance vectors”. After the weights and the noise variance are determined, the predictive mean
for a new input 𝑥∗ can be found as follows:
𝑓(𝑥∗ ) = 𝑤 𝑇
Φ∗.
(14)
In Eq.(14) Φ∗ = [1 𝐾(x∗
, r1) 𝐾(x∗
, r2) … 𝐾(x∗
, rNr)]T
where (r1, r2 … , rNr) are the
relevance vectors.

The total predictive variance can be found by adding the noise variance to the uncertainty due
to the variance of the weights, as follows:
𝜎∗
2
= 𝜎 𝑛
2
+ Φ∗
T
CΦ∗.
(15)
3. Construction of the Ground Motion Model
In this section, RVM regression algorithm will be used to construct a ground motion model. In
Section 4, the resulting model will be compared to an existing parametric model by Idriss (Idriss,
2008), which will be referred to as “I08 model” in this paper. To enable a fair comparison, the
dataset and the predictive variables of I08 model have been adopted in this study. The RVM
algorithm is independent of the size of the predictive variable set; additional variables can be
introduced the set of predictive variables can be customized to specific applications.
3.1 Ground Motion Data
The ground motion records used in the training have been obtained from the PEER-NGA
database (PEER, 2007). Consistent with the I08 model, a total of 942 free-field records have been
selected using the following criteria:
• Shear wave velocity at the top 30 m (𝑉𝑠30) ranging from 450 m/s to 900 m/s,
• Magnitude larger than 4.5,
• Closest distance between the station and rupture surface (R) less than 200 km.
Detailed information regarding these records can be found in the paper by Idriss (Idriss, 2008).
3.2 Predictive and Target Variables
The predictive variable set includes moment magnitude (M), natural logarithm of the closest
distance between the station and the rupture surface in kilometers (𝒍𝒏𝑅) and fault mechanism (F).
Idriss finds that with the shear wave velocity (𝑽 𝒔𝟑𝟎) constrained to 450 m/s- 900 m/s range, it has
31

negligible effect on spectral values up to 1 second. Therefore, 𝑽 𝒔𝟑𝟎 was not used as a predictive
variable. Following the convention used in I08 model, earthquakes that have been assigned a fault
mechanism type 0 and 1 in the PEER database were merged to a single, “strike-slip” group, while
the rest were considered to be representative of “reverse” events. In the RVM model, strike-slip
and reverse earthquakes are assigned 𝐹 = −1 and 𝐹 = 1, respectively. The input vector
representing ith
record has the following form:
𝑥𝑖 = [𝑀𝑖 𝑙𝑛𝑅𝑖 𝐹𝑖]. (16)
A set of eight vibration periods (𝑛𝑇 = 8) ranging from 0.01 second to 4 seconds was used in
the RVM model. The output for the ith
record for the vibration period 𝑇𝑗 is defined as:
𝑦𝑖 = 𝑙𝑛𝑆(𝑇𝑗) for 𝑗 = 1 to 𝑛𝑇. (17)
In Equation (17), 𝑙𝑛𝑆 is the natural logarithm of the average horizontal component of 5%-
damped pseudo-acceleration response spectrum. The spectral values(𝑆) represent the median
value of the geometric mean of the two horizontal components, computed using non-redundant
rotations between 0 and 90 degrees (Boore, 2006).
3.3 Training of the RVM Regression Model
As a pre-processing step, 𝑀 and 𝑙𝑛𝑅 values were linearly scaled to [-1 1] to achieve
uniformity between the ranges of the predictive variables. There is no need to scale the fault
mechanism identifier (𝐹) as it was already defined to take either -1 or 1. Because kernel functions
use Euclidean distances between pairs of input vectors, such scaling will help prevent numerical
problems due to large variations between the ranges of the values that variables can take. In the
ground motion data used in this study, the ranges of the predictive variables are
4.53 ≤ 𝑀 ≤ 7.68 , and 0.32 𝑘𝑚 ≤ 𝑅 ≤ 199.27 𝑘𝑚. Therefore, input scaling takes the
following form:

𝑥∗
= �
2𝑀∗
− 12.21
3.15
,
2𝑙𝑛𝑅∗
− 4.16
6.44
, 𝐹∗
�. (18)
The optimal value of the kernel width parameter (𝛾) for each vibration period was
determined using 10-fold cross validation (Webb, 2002). In 10-fold cross validation, the training
data is randomly partitioned into 10 subsets of equal size; and the model is trained using 9 subsets,
and the remaining subset is used to compute the validation error. This process is repeated 10 times,
each time with a different validation subset, and the average validation error for a particular 𝛾 is
computed. By computing the average validation error over a range of possible 𝛾 values, the
optimal 𝛾 with the smallest average validation error is determined. The resulting 𝛾 values for
each period are listed in Table 1, along with the standard deviation of noise (𝜎 𝑛), the mean value of
the constant term (𝑊0) and the number of relevance vectors. The relevance vectors and the
combination weights (𝑊𝑖) are listed in Table 2.
After the RVM models, one for each vibration period, were trained, standardized residuals
were computed. Figure 1 shows the distribution of the standardized residuals, corresponding to
T=1 second, with respect to 𝑴, 𝑹 and 𝑽 𝒔𝟑𝟎. The residual distribution patterns for other periods
were similar, not indicating any systematic bias.
Table 1: Kernel width parameter (𝛾), logarithmic standard deviation of noise (𝜎 𝑛), mean value of
the bias term(𝑊0) and the number of relevance vectors (𝑁𝑟), for each period.
T (sec) 𝛾 𝜎 𝑛 𝑊 𝑜 𝑁 𝑟
0.01 0.23 0.633 -3.069 7
0.05 0.32 0.666 -0.664 7
0.10 0.13 0.718 0.002 7
0.20 0.15 0.661 -15.042 6
0.50 0.25 0.695 -8.359 7
1.00 0.36 0.748 -4.670 5
2.00 0.28 0.869 -6.0548 5
4.00 0.26 0.983 -7.794 5
33

Figure 1: Standardized residuals for T=1 second.
Table 2: Mean values of the combination weights (𝑊𝑖) and the relevance vectors (𝑥𝑖)
T=0.01 s. T=0.05 s.
i Wi ri i Wi ri
1 13.258 [-0.1937 0.2676 -1] 1 -6.177 [0.7905 -0.4227 1]
2 15.393 [0.5238 -0.2268 1] 2 6.355 [-0.3841 -0.1783 -1]
3 0.4861 [ 0.8921 0.9414 -1] 3 28.555 [0.5238 0.5856 1]
4 -5.073 [0.9619 -1.0000 1] 4 -7.930 [-0.5111 0.7896 -1]
5 -4.275 [0.9619 -0.6751 1] 5 -0.402 [0.7460 -0.4021 -1]
6 -14.173 [-0.2889 0.7862 -1] 6 -12.622 [0.9619 0.9545 1]
7 -8.086 [ 0.0603 0.9789 1] 7 -16.194 [0.0603 0.9789 1]
T=0.1 s. T=0.2 s.
i Wi ri i Wi ri
1 64.423 [0.4159 -0.1499 1] 1 29.569 [-0.8921 -0.0837 -1]
2 -6.991 [ 0.9619 0.9545 1] 2 2.293 [0.7905 -0.4227 1]
3 -36.297 [0.9619 -1.0000 1] 3 35.440 [0.8921 0.6543 -1]
4 15.875 [1.0000 0.4559 -1] 4 5.7412 [0.9619 -1.0000 1]
5 -5.599 [-0.3143 0.0809 1] 5 3.5036 [-0.8222 0.1385 1]
6 -17.361 [ 0.6508 0.9961 -1] 6 -48.496 [0.0603 0.4955 -1]
7 -25.799 [-0.1302 0.9056 1]

Table 2 (continued).
T=0.5 s. T=1.0 s.
i Wi ri i Wi ri
1 6.4551 [0.7905 -0.4227 1] 1 1.9699 [0.7905 -0.4227 1]
2 12.825 [-0.2317 -0.2931 -1] 2 4.8873 [0.0540 -0.2785 -1]
3 0.0283 [-0.7714 0.1214 1] 3 -4.1425 [-0.7524 0.7892 1]
4 -0.806 [ 0.8921 -0.0318 -1] 4 -3.9593 [-0.7651 0.8672 -1]
5 8.4335 [0.8921 0.9414 -1] 5 3.7352 [-0.1302 -0.0121 1]
6 -0.089 [ 0.9619 0.9545 1]
7 -12.9 [ 0.0603 0.5786 -1]
T=2.0 s. T=4.0 s.
i Wi ri i Wi ri
1 7.3574 [-0.2317 -0.2931 -1] 1 0.4747 [0.7460 -0.4021 -1]
2 4.5548 [-0.0730 0.4691 1] 2 11.936 [0.7460 0.5118 -1]
3 3.0086 [ 0.9619 -1.0000 1] 3 6.8109 [0.3714 -0.0296 1]
4 -6.4695 [-1.0000 0.5142 -1] 4 -5.6050 [-0.7524 0.7892 1]
5 -5.3630 [-0.7524 0.7892 1] 5 -10.180 [0.3778 1.0000 -1]
3.4 Prediction Phase
After training, the spectral values for a new input vector 𝑥 = [𝑀, 𝑙𝑛𝑅, 𝐹 ] can be determined
as follows:
1. Scale the input to the range [-1 1] using Eq. (18);
2. Construct the basis vector Φ∗ = [1 𝐾(𝑥∗
, 𝑟1) 𝐾(𝑥∗
, 𝑟2) … 𝐾(𝑥∗
, 𝑟 𝑁𝑟)]T
using the
relevance vectors from Table 2 and the kernel width parameter from Table 1;
3. Determine the median value of 𝑙𝑛𝑆 using Eq.(14);
4. Obtain the standard deviation of the noise from Table 1. Total uncertainty, if needed, can
be determined using Eq.(15).
4. Computational Results
The RVM model was tested using different magnitude, distance and fault mechanisms, and the
results were compared to the I08 model. Figure 2 shows the median spectral acceleration at T=1
35

second, along with the 16th
and 84th
percentile values (±𝜎 𝑛 bounds) for strike-slip faults, for
M=5 (left) and M=7 (right). The circles in the figure show the spectral values from earthquakes
with the same fault mechanism and within ±0.25 magnitude units. Figure 3 shows the same
information for reverse faults. For periods about 1 second and longer, it was observed that the
median estimates from the RVM model were generally lower than those from the I08 model. At
very short distances, within ~20 km of the source, RVM estimates were higher for M=7, for both
strike-slip and reverse faulting earthquakes.
Figure 2: Median ±σ bounds for spectral acceleration at T=1 second, strike-slip faults.
Figure 3: Median ±σ bounds for spectral acceleration at T=1 second, reverse faults.

Figure 4 presents the results for vibration period T=0.2 second, for strike-slip earthquakes.
The results for the reverse faulting earthquakes were similar. For shorter vibration periods, and
M=7, RVM estimates were lower than those from the I08 model. For M=5, however, RVM
predictions equaled or exceed the I08 predictions. Regarding the variation about the median (noise
variance), the predictions from the two models were in general agreement for all vibration periods.
Figure 4: Median ±σ bounds for spectral acceleration at T=0.2 second, strike-slip faults.
5. Conclusion
This paper proposes an RVM-based model for the average horizontal component of
earthquake response spectra. Given a set of predictive variable set, and a set of ground motion
records, the RVM model predicts the most likely spectral values in addition to its variability. An
example application has been presented where the predictions from the RVM model have been
compared to an existing, parametric ground motion model. The results demonstrate the validity of
the proposed model, and suggest that it can be used as an alternative to the conventional ground
motion models.
The RVM model offers the following advantages over its conventional counterparts: (1) There
is no need to select a fixed functional form. By determining the optimal variances associated with
37

the weights, the RVM automatically detects the most plausible model; (2) The resulting RVM
model has a simple mathematical structure (weighted average of exponential basis functions), and
is based on a small number of samples that carry the most relevant information. Samples that are
not well supported by the evidence (as measured by the increase in the marginal likelihood) are
automatically pruned. (3) Because the model complexity is controlled during the training stage, the
RVM has lower risk of over-fitting.
One limitation of the proposed approach is that the resulting model may be difficult to
interpret. Because the RVM is not a physical model, it does not allow any user-defined, physical
constraints, not allowing extension of the model to scenarios not represented in the training data
set. However, in our opinion, this does not constitute a shortcoming, considering that the reliability
such practice is questionable in any regression model. Another potential limitation is that the RVM
requires a user-defined kernel width parameter, which does not have a very clear intuitive meaning,
especially when working with high dimensional input vectors. However, the optimal value of the
kernel width parameter can be determined using cross-validation, as has been done in this study.
Future studies will investigate the effect of using additional predictive variables on the
performance of the model.
6. Acknowledgements
This material is based in part upon work supported by the National Science Foundation under
Grant Number CMMI-1100735.
7. References
Boore, D.M., J. Watson-Lamprey, and N.A. Abrahamson. (2006). Orientation-independent
measures of ground motion. Bulletin of the Seismological Society of America, 96(4A),
1502-1511.
Bozorgnia, Y. and K. W. Campbell. (2004). The vertical-to-horizontal response spectral ratio and
tentative procedures for developing simplified V/H and vertical design spectra. Journal of
Earthquake Engineering, 8(2), 175-207.
Campbell, K. W. and Y. Bozorgnia. (2003). Updated Near-Source Ground-Motion (Attenuation)
Relations for the Horizontal and Vertical Components of Peak Ground Acceleration and
Acceleration Response Spectra. Bulletin of the Seismological Society of America, 93(1),
314-331.

Drucker, H., C. J. C. Burges, L. Kaufman, A. Smola and V. Vapnik. (1997). Support vector
regression machines, Advances in Neural Information Processing Systems 9, MIT Press.
Idriss, I. M. (2008). An NGA empirical model for estimating the horizontal spectral values
generated by shallow crustal earthquakes. Earthquake spectra, 24(1), 217-242.
MacKay, D. J. C. (1992). Bayesian interpolation. Neural computation, 4(3), 415-447.
MacKay, D. J. C. (1992). The evidence framework applied to classification networks. Neural
Computation, 4(5), 720-736.
PEER. (2007). PEER-NGA Database. http://peer.berkeley.edu/nga/index.html.
Smola, A. J. and B. Schölkopf. (2004). A tutorial on support vector regression. Statistics and
Computing, 14(3), 199-222.
Tezcan, J. and Q. Cheng. (2011). A Nonparametric Characterization of Vertical Ground Motion
Effects. Earthquake Engineering and Structural Dynamics (in print).
Tezcan, J., Q. Cheng and L. Hill. (2010). Response Spectrum Estimation using Support Vector
Machines, 5th International Conference on Recent Advances in Geotechnical Earthquake
Engineering and Soil Dynamics, San Diego, CA.
Tipping, M. (2000). The relevance vector machine. Advances in Neural Information Processing
Systems MIT Press.
Webb, A. (2002). Statistical pattern recognition, New York, John Wiley and Sons.
Dr.Jale Tezcan is an Associate Professor in the Department of Civil and Environmental
Engineering at Southern Illinois University Carbondale. She earned her Ph.D. from Rice University,
Houston, TX in 2005. Dr.Tezcan’s research interests include earthquake engineering, material
characterization, and numerical methods.
Dr.Qiang Cheng is an Assistant Professor in the Department of Computer Science at Southern
Illinois University Carbondale. He earned his Ph.D. from the University of Illinois at Urbana
Champaign, IL in 2002. Dr.Cheng’s research interests include pattern recognition, machine
learning and signal processing.
39

Influence of Carbon in Iron on Characteristics of
Surface Modification by EDM in Liquid Nitrogen
Apiwat Muttamara
a*
, Yasushi Fukuzawa
b
a
Department of Industrial Engineering Faculty of Engineering, Thammasat University, THAILAND
b
Department of Mechanical Engineering Faculty of Engineering, Nagaoka University of Technology,
JAPAN
Article history:
Received 23 August 2011
Received in revised form
23 September 2011
Accepted 26 September 2011
Available online
26 September 2011
Keywords:
EDM,
Surface modification
Titanium nitride,
Liquid nitrogen.
Many surface modification technologies have been proposed
and carried out practically by CVD, PVD et.al. Carbonized layer has
been made using EDM method. In this paper, to make the nitride
layer by EDM some new trials were carried out using a titanium
electrode in liquid nitrogen. Experiments were carried out on carbon
steel (S45C), pure iron and cast iron. TiN can be obtained on EDMed
surface. Moreover, TiCN can be found on cast iron and steel (S45C)
by XRD investigation. To confirm the fabrication mechanisms of
modified layer on the steel, the following experimental factors were
investigated by EDS.
1. Introduction
Many surface modification technologies have been proposed and carried out practically by
CVD, PVD et.al. Surface modification by EDM have been succeeded to make the modified layer
2011 American Transactions on Engineering & Applied Sciences.2012 American Transactions on Engineering & Applied Sciences
*Corresponding author (A.Muttamara). Tel/Fax: +66-2-5643001 Ext.3189. E-mail
address: mapiwat@engr.tu.ac.th 2012 American Transactions on Engineering &
Applied Sciences. Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660 Online
available at http://TUENGR.COM/ATEAS/V01/41-55.pdf
41

i.e. TiC, Si, WC etc. on the work piece by EDM method (N.Saito et.al.,1993). In this method, the
carbon element that is supplied from the dissolution phenomena of working oil during discharges
reacts with the electrode element of Titanium. When the compacted powder body used as an
electrode, TiC products piled up easily on the steel surface. On the other hand, the surface modified
TiN can be achieved with titanium electrode in liquid nitrogen. (Muttamara et al.,2002). Biing
Hwa Yan et al., 2005, carried out EDM in urea solution in water with Ti electrode and obtained
TiN machined surface. It is interesting that carbon come off by reverse diffusion from the
workpiece to the recast layer (Marash et al., 1965). Therefore, the surface modified TiN and TiCN
layers have attracted interest for workpiece materials which have high carbon content such as
carbon steel and cast iron. Although hardness of TiN layer is lower than TiC layer but friction
co-efficiency of TiN layer is quite stable and quite low. In this paper, a new modification method of
nitride modified layer on steels by EDM in liquid nitrogen using a titanium electrode is proposed.
2. Experimental procedure
Figure 1 shows the illustrated experimental set up. The machining was carried out in liquid
nitrogen on carbon-steel (S45C), pure iron and cast iron. Cylindrical Ti solid was applied as an
electrode. Table 2 shows chemical composition of S45C. Table 3 shows chemical composition of
pure iron and cast iron. The discharge waveforms were observed with a current monitor to analyze
the discharge phenomena on this machining.
Figure 1: Experimental Set up for EDM in liquid nitrogen.
Ti electrode
Workpiece
Ground
Oscilloscope
Control circuit Current Detector
Liquid Nitrogen
Electrical
power
source Vessel
42 Apiwat Muttamara, and Yasushi Fukuzawa

Table 1 : Properties - PVD coating Datasheet.
Coating
Material
Colour Key Characteristics Hardness
(Vickers)
Maximum
Working
Temperature
Friction
Coef
(on dry steel)
TiN Gold Good general purpose 2300 600C 0.4
TiC Grey High hardness 3500+ TBD >0.1
TiCN Blue Gray
Perple
High hardness, good
wear resistance,
enhanced toughness
3000 400C 0.4
Table 2 : Chemical composition of S45C (mass%)
C Si Mn P S Fe
0.45 0.2 0.77 0.17 0.25 Bal.
Table 3 : Chemical composition of pure iron and cast iron (%)
Workpiece C (%) Si (%) Fe
Pure iron <0.005 0 Bal.
Cast Iron 2.11-4.5 3.5 Bal.
Table 4 : The experiment conditions
Parameters Values
Polarity (Electrode) -
Current (A) 10, 47
On-time (μs) 32,512
Duty factor (%) 11,50
Open circuit voltage, ui (V) 220
Water pressure (kg/cm2
) 40
Spindle speed (rpm) 500
43

The machining characteristics are estimated in terms of surface roughness, Vicker’s hardness,
surface layer thickness, X-ray diffraction pattern, EPMA and EDS analysis. The machining
conditions are shown in Table 4. The special vessel was designed by polystyrene material for the
machining in the liquid nitrogen.
3. Results and discussions
At room temperature, liquid nitrogen holds as a boiling state in the vessel. It is known that
when the discharge occurs in boiled working medium, the machining phenomena are affected by
the bubble generation and the a few discharges contribute to the machining state. Further,
exploding the vapor bubble and causing the molten metal to difficult be expelled from the
workpiece so that only piling process occurs without machining process. To investigate the pulse
discharges in liquid nitrogen, discharge waveforms were observed. Figure 2 shows the discharge
waveforms in liquid nitrogen. The detailed waveforms were indicated as A` and A line in Figure 2,
are shown in Figure 3. The experiments of EDM were performed on the surface of S45C.
Machining conditions were as follows: negative polarity, ie=10A, te=32µs, D.F.=50%. There are 4
types waveforms: (a) normal, (b) short, (c) concentrate, (d) short eliminated current. Due to liquid
nitrogen holds as a boiling state, therefore EDMed in liquid nitrogen requires a time to break down
into ionic (charged) fragments, allowing an electrical current to pass from electrode to workpiece.
This region was named as an ignition delay time. Many shorts and concentrate discharges occurred
in this process. It can be explained that the sludge was made by the gathering debris phenomena in
the gap space during the short circuit and piled on the machined surface during ignition delay time.
When the electrode touches the workpiece through the sludge, the concentration of discharge pulse
and short circuit occurs. It assumed that the surface modified layer was fabricated by these special
discharge phenomena. When short occurs in EDM, it tends to continue long time such as several
100ms from several 10ms. To solve the problem, our EDM system automatically lunches eliminate
current to the process (Goto A.et al.,1998). As Figure shows, during off-time it is checked whether
gap is short, next pulse is eliminated.

Figure 2: Discharge waveforms in liquid nitrogen.
Figure 3: Normal discharge and concentrate discharge in period A`– A.
3.1 Effect of electrode polarity
On the normal EDM, the positive (+) electrode polarity is chosen for the machining (Janmanee
P. and Muttamara A.,2011). On the contrary, the negative polarity (-) often uses for the modified
technology (N.Saito et.al.,1993), (Muttamara et al.,2004), and also machines for insulating
ceramic materials (Muttamara et al.,2009-2010). These experiments were done under the
Concentrate
A’
A
Discharge voltage (ue)= 15V
Normal
10
Current
0V.
80V.
Voltage
0A
50 µs/div
Time 0.5ms/div
A’
A
1
Current
0V
80V
Voltage
0
Short
Ignition delay time
Eliminate current
45

following machining conditions: ie=10A, te=32µs, D.F.=11.1% with Ti solid electrode ofφ5mm.
Figure 4 shows the shape of electrical discharge marks from a single pulse electrical discharge
experiment in which all other conditions are identical, and only the polarities are changed.
a) Positive b) Negative
Figure 4: Single crater created by a) positive and b) negative polarity.
It can be seen that in the case of negative polarity, large amounts of the melted electrode
implant to the workpiece. In comparison, in case of positive, a relatively clean surface crater is
formed. Judging from the result, the negative polarity was selected.
3.2 EDM on S45C
To study characteristics of modified layer, the cross sectional of nitride product modified layer
on S45C was observed by laser microscope and EPMA analysis. Figure 5 (a),(b) and (c) show the
cross sectional EDMed surface by laser microscope, EPMA map analysis and EPMA line analysis
of cross sectional EDMed surface, respectively. The golden colored layer could be observed on the
machined surface. The characteristics of the modified layer were investigated by the
micro-hardness Vickers using a load of 10gf and the EPMA analysis. Figure 6 shows
micro-hardness distribution on the cross section of modified layers with solid and semi-sintered.
(ie=10A., te=32µs, D.F.=11.11%). On the machining of Ti solid electrode, there were three areas:
(1) nearest surface region, 0-50 µm, the hardness reached to 1300HV that corresponded almost to
the same value of other report (table 3.1), (2) thermal affected region, 50-100 µm: similar hardness
of martensite structure of 800HV, (3) original substrate region: over 100 µm. On the contrary, the
hardness of region (1) became the same value, 800HV at region (2) on the machining of
semi-sintered electrode.

EPMA analysis of Ti, N and C, was carried out on the cross sectional modified surface. The
distribution of Ti and N element was divided to three regions same as Figure 5. The distribution of
Ti and N element was detected from region (1) to (2). It indicated that the region composed with the
thermal affected structure of substrate and the diffused TiN products. In the (1) and (2) region, the
higher carbon element was observed than matrix regardless no supplying source around discharge
circumstances. Because carbon was observed on the modified layer on S45C. It was thought that
carbon come off by reverse diffusion (Barash et al.,1965).
a) Modified layer on S45C in liquid nitrogen
b) EPMA Map analysis Modified layer on S45C in liquid nitrogen
continue Figure 5 on next page
Line
analysis
Modified layer
40
Area
47

c) EPMA Line analysis
Figure 5: Cross sectional image of TiN layer on S45C by a) Laser Microscope
b) EPMA Map analysis c) EPMA Line analysis.
Figure 6 : Relationship between micro-hardness Vickers against the cross section of modified
layer on S45C.
3.3 EDM on Pure iron
Pure Iron does not contain carbon (less than 0.005%). The concentration of substances on the
cross section of modified surface on pure iron were carried out with Ti solid. Figure 7 shows
cross sectional SEM of EDMed surface on pure iron compared with EPMA results. Figure 8
shows the sectional micro-hardness measurements of modified surface. The thickness of modified
layer is 100 µm as same as the modified layer on S45C. From the sectional micro-hardness result,
50 100 150 2000
Distance from top surface (µm)
200
400
600
800
1000
1200
1400
Modified layer
Hardness(HV)
Ti N C
1600 240 40
800 120 20
Int (Count)
0 50 100 150 250
C
N
Modified layer
T

hardness of modified surface is 600-800 HV. The hardness of modified layer on Fe is lower than
that on S45C. This is considered that carbon in the material of S45C affect to the compound of
modified layer.
a) SEM of TiN layer on pure iron b) EPMA Line Analysis
Figure 7: Cross sectional TiN layer on Fe a) SEM and b) EPMA Line Analysis
Figure 8: Micro-hardness distribution (EDM Conditions; ie=47A, te=256µs, D.F.= 11.1%).
3.4 EDM on cast iron
Cast iron was used to confirm (reverse) diffusion of carbon. In this experiment, discharge
current (ie)=47A, discharge duration (te)=256µs, (D.F.)=11.11%, were selected for EDMed
condition. Figure 9 shows cross sectional SEM of EDMed surface on cast iron compared with
EPMA results. Figure 10 shows the sectional micro-hardness measurements of modified surface.
100 200 300 400 500
1000
Hardness(HV)
800
200
600
0
400
Modified layer
Line analysis
100 µm 100 200
Modified layer
Int (Count)
Ti
N
Ti N C
600 800 20
300 400 10
0
C
49

100 200
Modified layer
Int (Count)
Ti
N
Ti N C
600 800 20
300 400 10
0
C
a) SEM of TiN layer on cast iron b) EPMA Line Analysis
Figure 9: Cross sectional TiN layer on cast iron a) SEM and b) EPMA Line Analysis
Figure 10: Micro-hardness distribution (EDM Conditions; ie=47A, te=256µs, D.F.= 11.1%)
The C and N elements concentrations are measured on the modified layer, distance of the
generation of C and N elements are 250 µm of modified layer as can seen from the Figure 9. First,
it should be noticed that system experiment was decarburizing. So carbon on modified layer should
come from the precipitated graphite in the cast iron. However, we cannot see clearly on EDS result
of carbon. Etching was done on cross section surface of cast iron as shown in Figure 11.
100 200 300 400 5000
800
200
600
1000
400
Modified layer
Hardness(HV)
100 µm
Line analysis

Figure 11: SEM micrographs of etched cross section surface of cast iron
The low part represents the base material, the central part in the curve mark represents the base
material that effect from heat affected zone (HAZ), and carbon diffused zone. The modified layer
was generated irregularly. The dendritic parts in substrate are graphite exist in the form of flakes. It
is pointed out that some areas inside close line carbon are depressed. The large scale of structure
(1)
(2)
20 µm
(2)(1)
HAZ
20 µm
51

under modified surface is shown in Figure 11 (a) Also the structure of normal graphite in cast iron
is shown in Figure 11 (b). The presences of graphite in HAZ (a) are different from normal content
(b). Therefore, it is considered that precipitated carbon diffuses by discharges or the changing of
structure of case iron.
Figure 12: Section hardness of machined surface before and after annealing
To investigate effect of carbon and HAZ on the hardness, the hardness was evaluated on cross
sectional of cast iron. Figure 12 shows the sectional hardness measurement of modified surface on
cast iron. It can be considered that the machined surface is covered with TiN and TiCN layer. The
hardness of modified layer is about 1450 Hv. On HAZ region, the hardness decreases gradually
according to the distance from the surface. It reaches to the hardness of matrix cast iron through
that of requenched region. Some hardness regions on HAZ are below the hardness of matrix region,
it is considered that the coming off of carbon effects to the hardness of that region. HAZ.
3.5 X ray-diffraction (XRD) analysis
As mentioned above, the some modified layer could be adhered on the work piece by EDM in
liquid nitrogen. To confirm the layer composition X ray-diffraction (XRD) pattern was
investigated for the EDMed surface with Ti solid electrode. Figure 13 shows the result of XRD on
EDMed surface on S45C compared with EDMed surface on pure iron and cast iron. The peak of
TiN and TiCN are very near. From the EPMA results and the hardness results, it indicates that the
EDMed surface on S45C and cast iron are composed of TiN and TiCN. On the other hand, only
TiN layer was observed on the EDMed surface of pure iron.
50
1000
1500
2000
200 400 600 800
Depth below surface (mm)
Microhardness(HV)
Modified layer HAZ
+ Diffused zone
Matrix
Depth below surface (µm)

Figure 13: X-ray diffraction patterns obtained from the EDMed layer in liquid nitrogen
by solid Ti on a) S45C , b) pure iron and c) cast iron.
a) EDMed surface on S45C
30 40 50 60 70 80
Diffraction angle 2θ (Cu Kα)
Fe
(CPS)
1000
500
Fe
Fe
TiN
TiCN
TiCN
TiN
TiCN
TiN
TiNTiN
c) EDMed surface on cast iron
30 40 50 60 70 80
Fe
(CPS)
1000
500 Fe
Fe
TiN
TiCN
TiCN
TiN
TiCN
TiN
TiN
TiN
b) EDMed surface on pure iron
1
(
CPS)
30 40 50 60 70 80
Fe1000
500
Fe Fe
TiN
TiN
TiN TiNTiN
53

4. Conclusion
A new EDM surface modification method was tried in liquid nitrogen on S45C steel in various
conditions. The results were summarized as follows:
(1) In liquid nitrogen, machining process is not obtained, but the TiN products adhere on the
work piece.
(2) Ti and N element diffused from nearest surface to the thermal affected zone.
(3) Discharge causes carbon migration from deeper layers of the substrate.
(4) TiCN modified layer could be generated on carbon steel and cast iron because carbon from
substrate diffused to modified layer and reacted with nitride product of modified layer.
5. Acknowledgement
The authors are grateful to Faculty of Engineering, Thammasat University, the National
Research Council of Thailand (NRCT), the Thailand Research Fund (TRF) and the National
Research University Project of Thailand Office of Higher Education Commission for the research
funds and T. Klaykaow for carrying out this work.
6. References
Barash, M.M.(1965). Effect of EDM on the surface properties of tool and die steels. Metals
engineering quarterly, 5, (4), 48-51.
Biing H.Y., Tsai H.C., Huang F. Y. (2005).The effect in EDM of a dielectric of a urea solution in
water on modifying the surface of titanium. International Journal of Machine Tools and
Manufacture, 45, (2), 194-200.
Fredriksson G., and Hogmark S., (1995). Influence of dielectric temperature in EDM of hot
worked tool steel. Surface Engineering, 11, (4), 324–330.
Goto A., T. Magara, T. Moro, H. Miyake, N. Saito, N. Mohri.(1997). Formation of hard layer on
metallic material by EDM. Proceedings of the ISEM-12, 271–278.
Goto, A., Yuzawa, T., Magara, T., and Kobayashi, K. (1998). Study on Deterioration of Machining
Performance by EDMed Sludge and its Prevention. IJEM, 3,1-6.
Mohri N., Fukusima Y., Fukuzawa Y., Tani T., and. Saito N.(2003). Layer Generation Process on
Work-piece in Electrical Discharge Machining, Annals of the CIRP, 52(1),161-164.
Mohri, N., Saito, N., and Tsunekawa, Y. (1993). Metal Surface Modification by EDM with
Composite Electrode. Annals of the CIRP, 42, (1) 219-222.

Muttamara A., Fukuzawa Y., Mohri N., and Tani T. (2009). Effect of electrode Materials on EDM
of Alumina. Journal of Materials Processing Technology, 209, 2545-2552.
Muttamara A., Janmanee P., and Fukuzawa Y.(2010). A Study of Micro–EDM on Silicon Nitride
Using Electrode Materials. International Transaction Journal of Engineering,
Management, & Applied Sciences & Technologies. 1(1), 1-7.
Janmanee P., and Muttamara A.(2011). A Study of hole drilling on Stainless Steel AISI 431 by
EDM Using Brass Tube Electrode. International Transaction Journal of Engineering,
Management, & Applied Sciences & Technologies. 2(4), 471-481.
Muttamara A., Fukuzawa Y., and Mohri N.(2002). A New Surface Modification Technology on
Steel using EDM, Journal of Australian Ceramic Society (38), 2,125-129.
Dr.Apiwat Muttamara is an Assistant Professor of Department of Industrial Engineering at
Thammasat University. He received his B.Eng. from Kasetsart University and the D.Eng. in
Materials Science from Nagaoka University of Technology, Japan. Dr. Muttamara is interested
involve Electrical Discharge Machining of insulating materials.
Yasushi FUKUZAWA is Professor of Material Science and Engineering group in Department of
Mechanical Engineering at Nagaoka University of Technology, Japan. Prof. Dr. Fukuzawa’s fields
are material processing and treatment.
55

ATEAS V1(1):: American Transactions on Engineering & Applied Sciences

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