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have used 3-D finite element models to simulate roller
expansion of tube–tubesheet joints (Williams 1997;Metzger
et al. 1995). These models which are more realistic provide
more in-depth information about the displacement and stress
distributions in all directions Williams however, concluded
that the 3-D model did not bring any additional information
when compared to axisymmetric model (Williams 1997).
To the authors’ knowledge the effect of tube–tubesheet
initial clearance on the strength of tube/tubesheet joint has
not been addressed by 3-D FE analysis of roller expansion.
Existing work has relied mainly on axisymmetric models
with hydraulic expansion (Allam et al. 1998) or with roller
expansion (Al-Aboodi et al. 2008, 2009; Cizelj and Mavko
1995; Williams 1996).
In this paper, a 3-D FE model has been utilized in a
major commercial finite element analysis code (ANSYS
2004) to simulate the roller expansion and study residual
deformation and stress distributions to show the effect of
initial clearance and tube material on the residual contact
pressure between the tube and tubesheet. Initial clearances
within and beyond the prescribed TEMA range (Standard
of the Tubular Exchanger Manufacturer Association
‘TEMA’ 1988) have been considered. Low-to-high tube
and tubesheet material strain hardening properties have
also been included in the study and their effects discussed
herein. The 3-D model results pertaining to the effect of
clearance on interfacial pressure are compared with those
obtained from the axisymmetric simulation of the same
effects and validated using experimental results developed
earlier by Shuaib et al. (2003).
Geometry and 3-D FE Model
The equivalent sleeve diameter determined earlier by
Shuaib et al. (2003) for the stabilizer feed/bottom
exchanger was implemented in the 3-D model. Figure 1a
illustrates the geometry and dimensions of the model of
tube–tubesheet joint under study. Figure 1b shows the full
3-D model mesh and Fig. 1c a 2-D view of the model with
boundary conditions on the primary side.Meshing of tube and tubesheet is performed using 3-D
structural solid element ANSYS-SOLID 186 which has a
quadratic displacement behavior and is well suited for
modeling irregular meshes. The element is defined by 20
nodes having three degrees of freedom each: translations in
the nodal x, y, and z directions. The element is chosen here
because it supports plasticity, hyperelasticity, and large
deflections. The model of Fig. 1b has 8,000 elements and
9,920 nodes. The level of refining was tested to establish
effective meshed models. It was found that refining the
mesh beyond 8,000 elements did not add any significant
precision to the solution.
The contact element CONTA174 is used to represent
contact and sliding between 3-D ‘‘target’’ surfaces
(TARGE170) and a deformable surface, defined by this
element. The element is applicable to 3-D structural and
coupled field contact analyses. This element is located onthe surfaces of 3-D solid elements with mid-side nodes. It
has the same geometric characteristics as the solid element
face with which it is connected. Contact occurs when the
element surface penetrates one of the target segment ele-
ments (TARGE170) on a specified target surface. A sen-
sitivity analysis was performed in order to select the real
constants values such as those defining tolerance and offset
between the contact and target elements (Al-Zayer 2001;
Al-Aboodi 2006).
Joint materials
The elastic–plastic behavior of tube and tubesheet material
is represented by bilinear curves. In the experimental work