7th International Research/Expert Conference
”Trends in the Development of Machinery and Associated Technology”
TMT 2003, Lloret de Mar, Barcelona, Spain, 15-16 September, 2003
THE EVALUATION PROCEDURE
OF BUTT WELD CRUCIFORM DETAIL
Željko Ivandić
Mechanical Engineering Faculty
Slavonski Brod
Croatia
Dražan Kozak
Mechanical Engineering Faculty
Slavonski Brod
Croatia
Milan Kljajin
Mechanical Engineering Faculty
Slavonski Brod
Croatia
ABSTRACT
Stress concentration factors for characteristic welded component applied in shipbuilding are
determined for different values of roundness radiuses by constant welded joint throat. For that
purpose finite element (FE) analysis has been applied. Due to FE results the evaluation procedure
was performed with the aim of an optimal shaping of the butt weld cruciform detail. Evaluation model
using theory of graphs enables us selection of an optimal design of the weld toe detail (5 different
roundness radiuses were changed). The final decision is based on the evaluation procedure, where
the main evaluation criterion was the value of stress concentration factor for any of proposed detail
solutions. The best solution from the set of five variant solutions was chosen applying the weight
functions. Proposed model can be extended varying the welded joint depths, what is directly
connected with needed welding time and the deposit price.
Keywords: butt weld cruciform, stress concentration factor, finite element analysis, evaluation
1. INTRODUCTION
In the conceptual phases of design it should be necessary to evaluate proposed variant solutions with
aim to choose the best solution [1]. This evaluation procedure is based on assigning grades to
particular design parameters of all acceptable solutions. The evaluation model presented in this work
includes mathematical formalisms of theory of graphs [2, 3]. As an example how to use the theory of
graphs to assess the acceptability level of one shipbuilding component with butt welded cruciform
joints [4] is presented in this paper. The radius roundness at the place of weld toe as only one design
parameter was changed. It could be expected that under nominal loading, stress concentration will
appear in the vicinity of toes. Therefore, an optimal shape of toe line due to stress distribution by
finite element analysis was analysed. Actually, stress distribution with its peak value may be used as a
parameter of goodness of component shaping. In this paper an optimal design of one characteristic
shipbuilding structure with butt weld cruciform has been investigated.
2. STRESS CONCENTRATION ANALYSIS BY BUTT WELD CRUCIFORM
Thin-walled characteristic shipbuilding component with butt welded cruciform joints has been chosen
[5] to investigate the influence of size of roundness radius r, which is measured at the weld face
between the filler metal and the parent metal on the stress distribution. The geometry of the
component and fillet welds with the throat thickness of 8 mm is given in the Fig. 1. Mechanical
properties of the material and its chemical composition are given in the ref. [5]. It is clear that stress
raise at the place where the fillet weld is attached to the component body.
r
r
50
o
8
10
90
Fillet weld
o
50
150
Stress concentration
at weld toe
80
Figure 1. Thin-walled welded shipbuilding component
All details of finite element modelling of ¼ of the component are given in the [4]. Stress distribution
was calculated by finite element analysis for five assumed radiuses roundness (r = 0, 1, 2, 4 and 8
mm). It has been shown that stress concentration factor (SCF) value becomes lower with radius of
roundness increasing. More rounded fillet weld at the place of touching with the parent metal causes
not only SCF decreasing, but removing the stress peak from the weld toe also.
3. EVALUATION PROCEDURE
First step by assessing of any particular variant solution is to create a hierarchical structure with all
criteria arranged by levels. Here, all performed component designs are loaded with the same nominal
stress and the only criterion was the radius of roundness. Of course, the greater value of r needs
untoward additional mechanical work and more deposit, but such detail performance increases
carrying capacity of the whole component. In this paper, well known theory of graphs is applied.
Generally, a directed and oriented graph G is determined as Gi  (V , R), i = 1, ..., n , where V is the
set of nodes, which are here SCFs in the function of the radiuses roundness r1 … r5 and R is the set of
relations between elements of the set V [6]. The graph G is determined by matrix of incidence B. Let
us to define the graph G ( SCF1 ,..., SCF5 ) , where the relation between particular SCFs (r1) is
quantitatively given by preferences  (Fig. 2).
1
SCF1
2
SCF2
3
4
2
2
SCF5
1
3
1
SCF3
1
SCF4
Figure 2. The graph of preferences between SCFs
The potential vector X is a real function X: V   . The potentials difference is the product of the
matrix of incidence and the potential vector. The components of potential vector are determined by
difference of potentials of the set V [2, 3]:
y 
Xu  Xv
.
 (u, v)
where u and v are the components of the set V.
... (1)
The set of potentials for all SCFs in the function of r may be shown as matrix:
 1,90 
 1,00 


 X SCF  r1 ,..., r5     0,10  .


 1,00 
 2,00 
... (2)
The matrix of incidence of the graph G ( SCF1 ,..., SCF5 )
1
1

1

1
0
B  
0
0

0
0

0
1 0 0 0 
0 1 0 0 
0 0 1 0 

0 0 0 1
1 1 0 0 
 .
1 0 1 0 
1 0 0 1 

0 1 1 0 
0 1 0 1 
0 0 1 1 
... (3)
The flow F is the result of the potentials difference of criteria, given by F: R   . Thus, the flow can
be written as F = B · X. The normal integral F is every solution of equation BT·B ·X = BT · F, Σ Xi=
0.
Let us to define the matrix A as:
A  B T
4
 1

 B   1

 1
 1
1
4
1
1
1
1
1
4
1
1
1
1
1
4
1
1
1
1 .

1
4 
... (4)
Abovementioned equation B T  B  X   Fr may be writen as A  X   F . Hence, the solution
of the flow difference of the normal integral F is given by:
A  X   F 
4
 1

 1

 1
 1
1
4
1
1
1
1
1
4
1
1
1
1
1
4
1
1  1,90   9, 48
1  1,00   5,00 
.
1   0,10    0,52   F
 
 

1  1,00   5,00 
4   2,00  10,00 
... (5)
From the vector of potentials X, the vectors of weights w are calculated: wi = aXi, i = 1, …, n. Weight
components vector influenced the priorities between analysed SCFs depending on different radiuses
roundness r. Norm vector of priorities must satisfy the condition: Σ wi = 1.
In our example, the weight matrix of the set of SCFs is calculated as:
 wSCF1  0,035


 

w
 SCF2  0,065 


WSCF    wSCF3    0,121  .
w
 0, 260 

SCF4

 

 wSCF   0,520 
5 

... (6)
According to the equation (6) one can conclude that wSCF5 = 0,52 presents the greatest value of the
component of norm vector of weights. Its value is calculated as:
w  SCF5   wSCF5 
a
5
X SCF 5
a
X SCF i

22,00
21,90  21,00  20,10  21,00  22,00
 0,520 . … (7)
i 1
This means that performed variant solution with the greatest radius of roundness r is most acceptable
solution. Of course, this conclusion should to be extended with variation of other important design
parameters to be able to make decision with highest accuracy.
4. CONCLUSIONS
The presented model of evaluation confirms previously shown finite element results in the analysis of
the influence of the roundness radius on the stress concentration factor by butt weld cruciform detail
of one shipbuilding component. Proposed model assures clearly defined procedure for grades
assignment 7, with the aim to rank all variant solutions. Highest value of the grade obtained by
evaluation procedure means the best solution. Theory of graphs as used method in this paper has been
successfully applied to assess the goodness of proposed variant solutions in the conceptual phase of
design. In this way, the final decision is quantitatively argued and the procedure of choice of most
acceptable solution is accelerated. However, the procedure given in this work should be understood
just as the basement for further complex investigation of all influenced design parameters in the
product development.
Acknowledgment
The authors would to thank to Prof Čaklović from the Faculty of Mathematics, University of Zagreb
for his help in theoretical background of theory of graphs introduction. The Ministry of Science and
Technology of Republic of Croatia financially supported the publication of this work through the
grant No 0152 015.
5. REFERENCES
[1] Green, G.: Evaluation activity in the Conceptual Phase of the Engineering Design Process, PhD
thesis, University of Glasgow, UK, 1994.,
[2] Čaklović, L.: Decision making via potential method, Accepted for the publication in Journal,
[3] Ivandić, Ž.: The Conceptual Evaluation of Design Parameters (in Croatian), Dissertation,
University of Zagreb, 2002.,
[4] Kozak, D, Ivandić, Ž.: Numerical determination of stress concentration factors and material
yielding factors for welded joints, Proceedings of the CIM 2001, Lumbarda, V:019-026, 2001.,
[5] Wagner, M.: Schwingfestigkeit geschweißter Konstruktionsdetails, Konstruktion, Juli/August 7/8,
1999.,
[6] Veljan, D.: Kombinatorna i diskretna matematika, Algoritam, Zagreb, 2001.,
[7] Kozak, D., Ivandić, Ž. and Kljajin, M.: Decision making model based on grading approach, ICIL
2003, Vaasa, In press.