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Distortion Analysis of Welded Stiffeners
O. A. Vanli , P. Michaleris
June 19, 2001
Abstract
This paper presents a welding distortion analysis approach for T-stiffeners with a particular
emphasis on welding-induced buckling instabilities. 2-D thermo-mechanical welding process
simulations are performed to determine the residual stress and angular distortion. The critical
buckling stress along with the buckling mode and bowing distortion are computed in 3-D
eigenvalue and linear stress analyses. The effects of the stiffener geometry, weld sequence, weld
heat input and mechanical fixturing on the occurance of buckling and the distortion pattern are
investigated.
Graduate Student, Department of Mechanical and Nuclear Engineering, 307 Reber Building, Pennsylvania State
University,University Park, PA 16802, USA Tel : (814) 865-0059, Email: [email protected] Professor, Department of Mechanical and Nuclear Engineering, 232 Reber Building, Pennsylvania State
University, University Park, PA 16802, USA Tel : (814) 863-7273 Fax : (814) 863-4848 Email: [email protected]
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1 Introduction
Welding, among all mechanical joining processes, has been employed at an increasing rate for
its advantages in design flexibility, cost savings, reduced overall weight and enhanced structural
performance. In this research, welding is being evaluated as the manufacturing method for stiffeners
as an alternative to the present fabrication method of cutting or stripping from standard I-
beams. Use of welding in stiffener fabrication may introduce considerable savings by eliminating
scrap parts.
Thinner section components made of higher strength steels are being commonly utilized in
shipbuilding, railroad and aerospace industries in fabricating large structures to achieve reduction
in overall weight and more controllable manufacturing. However, for the structures made of
relatively thin components, welding can introduce significant buckling distortion which causes loss
of dimensional control and increased fabrication costs due to poor fit-up between panels. Flame
straightening is the commonly used technique to correct the out-of-plane distortion resulting from
welding processes, and is a labor intensive and costly process.
Finite element techniques have been used in the prediction of welding residual stress and
distortion for more than two decades. Due to the nature of the process, additional complexities are
involved in the FEA of welding compared to traditional mechanics, such as temperature and history
dependent material properties; high gradients of temperature, stress and strain fields with respect to
both time and spatial coordinates; large deformations in thin structures and phase transformation
and creep phenomenon.
Most of the currently performed welding simulations, both 2-D and 3-D, are based on small
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deformation assumption and are limited to simpler structures and weld geometries (e.g. butt joints)
or focusing only to the heat affected zones, ignoring the surrounding structure. A small deformation
analysis assumes infinitesimal displacements and loads being applied to the undeformed geometry.
The interaction between the weld zone and the structure is effective on the accumulated distortion,
and large deformation modes in unrestrained structures may not be captured with this type of
analysis [1], [2]. Brown and Song [1] have performed 2-D axisymmetric and 3-D weld simulations
of a ring stiffened cylinder structure, and concluded that 2-D analysis overestimated the rotation
of the ring during the heating segment, and it was very sensitive to model modifications, such as
joint clearance and location of constraints. Michaleris et. al. [2] studied the effects of the restraints
and the solidified portions of the weld on the residual stress and distortion profiles by comparing
the performance of 2-D and 3-D weld simulations.
Earlier studies of welding accounted for the non-linearities due to temperature dependent
material properties and plastic deformations [3, 4, 5]. The majority of those analyses were
limited to two-dimensions on the plane perpendicular to welding direction, but good correlations
have been observed between the numerical predictions and experimental results [6, 7, 8, 9], and
especially for residual stress predictions, 2-D models provided accurate estimations comparable to
3-D analyses, since the stress field exhibits a fairly uniform distribution through the length of the
work-piece. Argyris et. al. [6] computed the thermo-mechanical response using 2-D models in a
staggered solution strategy to combine and integrate the thermal and mechanical computational
steps. Rybicki et. al. [7] performed thermo-elasto-plastic analysis on a 2-D axisymmetric finite
element model for a two-pass girth-butt welded pipe problem, and verified the numerical results
with the experimentally obtained temperature history and residual stress distributions. Papazoglu
and Masubuchi [8] solved the multipass GMAW process problem by performing uncoupled 2-D heat
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transfer and stress-strain analyses, incorporating the phase transformation strains.
2-D models, as mentioned above, have been particularly useful with their high efficiency and
accuracy in determining the solution in the analysis plane and reduced computational requirements.
However, for welding practices where tack welding or fixturing allow out-of-plane movement 2-D
analyses may not be accurate, particularly, in distortion predictions [1]. Furthermore, longitudinal
heat transfer and instability aspects, and end effects (i.e. due to initiation and termination of the
heat source) cannot be realized in two dimensional formulations.
Oddy et. al. [10] examined the butt welding of a bar via 3-D FEM, and computed the
temperature, strain and stress fields. Tekriwal and Mazumder [11, 12] simulated thermal and
elasto-plastic response of the butt-welded plates through 3-D models, considering filler material
addition. Multi-pass welding simulation of plates and experimental validation have been addressed
in [13, 14].
Welding-induced buckling of thin-walled structures has been investigated in greater detail by
[15, 16, 17]. Tsai et. al.[15] studied the distortion mechanisms and the effect of welding sequence on
panel distortion. Ueda et. al. [16, 18] presented a methodology to determine the buckling behavior
of plates by large deformation elastic FEA and employing inherent strain distributions.
For the welding practices where tack welds or fixturing are used to restrict the movement of the
welded parts, the structural response may be evaluated by means of decoupled 2-D welding and
3-D buckling simulations. When mechanical fixturing on the structure prevents the longitudinal
shrinkage during welding, the out-of-plane structural behavior doesnt have influence on the in-
plane welding response, and buckling is only observed after the restraints are removed and the
structure cools down. Exploiting this fact, Michaleris et. al. [17] proposed a method to predict
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welding-induced buckling by uncoupling the weld simulation and the structural buckling analysis.
They expressed the residual stress profile from the 2-D welding simulations as buckling stress on
the 3-D structural model. This approach is analogous to the work by Ueda et. al. [18], where the
concept of inherent strain is used to generate the welding residual stresses by applying a prescribed
thermal strain field using empirical methods. In the former study, however, residual stresses are
calculated with weld process simulations, which provides improved estimations for buckling analysis
compared to empirically determining the residual stress.
Phase transformations and transformation plasticity have also been incorporated in the analysis
as recent developments [10, 19, 20]. The primary objective there is to more accurately model the
residual stress distribution, microstructure and local distortion in the area immediately adjacent
to the weld.
In this work the decoupled 2-D and 3-D finite element analysis technique by Michaleris et.
al. [21, 17] is applied to evaluate welding-induced buckling of fabricated stiffeners. Effects of the
following process and design parameters are investigated,
stiffener cross-section (small section, large section),
fixturing and future stiffener straightening
(as weld, and rammed-down configurations),
Gas Metal Arc and Submerged Arc Welding processes,
simultaneous (offset-torch) and sequential welding processes.
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Figure 1: Distortion Modes in fabrication of stiffeners
2 Analysis Approach - Modelling the Welding Distortion
Following the work of Michaleris et. al. [21, 17], the response of the stiffener is evaluated in two
steps by combining two-dimensional welding simulations with three-dimensional structural analyses
in a decoupled approach.
2-D Thermo-mechanical Weld Simulation :
A two dimensional thermo-elasto-plastic analysis is performed to determine the angular
distortions, residual stresses, and plastic strain fields during the welding process ignoring the
structural response. Residual stresses are caused by the negative plastic strains resulting from
the welding thermal cycle.
3-D Eigenvalue and 3-D Linear Stress Analyses :
The buckling distortion and critical buckling stresses are consequently determined by an
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eigenvalue and a linear stress analysis applying the, mostly uniform and compressive, longitudinal
plastic strain field of the 2-D weld model on the 3-D structural model as equivalent load.
A constant, negative thermal load is applied at the weld region to introduce the effects of welding
into the 3-D structure. Thermal loading is used rather than mapping the plastic strain field, which
would require a complex analysis procedure. An eigenvalue analysis is performed to determine
the critical residual stresses and buckling distortions, and a linear stress analysis is performed to
compute the bowing distortion.
2.1 Modes of Welding Distortion
The structural response of the stiffener is evaluated in terms of angular, bowing and buckling
distortions as illustrated in Figure 1. The overall distortion of the structure will be a combination
of these distortion forms.
Angular Distortion: The angular distortion is the change in the included angle between the
web and the flanges on both sides (1, 2, Figure 2 ) and is computed by the 2-D welding simulation.
Bowing Distortion: The bowing distortion is the displacement of the web in y-direction (d,
Figure 3 ) due to bending of the stiffener about the x-axis, and is computed by the 3-D linear stress
analysis.
Buckling Distortion: The critical buckling and the corresponding mode shape of the structure
are determined in the 3-D eigenvalue buckling analysis.
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Figure 2: Angular Distortion of the stiffener flanges
Figure 3: Bowing Distortion of the stiffener
2.2 Welding Simulation
The welding simulation involves a thermal and a mechanical analysis. The effect of mechanical
response is assumed to be negligable on the thermal behavior, thus the temperature field is solved
independently from the mechanical solution. To determine the temperature history profile, a non-
linear, transient heat-flow finite element analysis is performed on the plane perpendicular to the
welding direction.
The numerical implementation of the history dependent (transient) heat transfer problem
involves an incremental scheme with several small time increments. The solution at a given time
increment is obtained by using the solution at the previous time increment as an initial condition.
This problem is addressed in detail in references [4, 22, 11].
The governing energy balance equation for transient heat transfer analysis is given as follows,
CpdT
dt(r, t) = r q(r, t) + Q(r, t) in the entire volume Vr of the material (1)
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Weld Qb [W] v [mm/s]
GMAW 9750 0.75 11.85
SAW 9000 0.90 10.16
Table 1: Weld Parameters
where is the density of the body ([kg/mm3]), Cp is the specific heat capacity ([J/kgoC]), T is the
temperature ([oC]), q is the heat flux vector, Q is the internal heat generation rate, t is the time,
r is the coordinate in the reference configuration and r is the spatial gradient operator.
The nonlinear isotropic Fourier heat flux constitutive relation is enforced; using the temperature-
dependent thermal conductivity, k ([ WoCmm2 ]),
q = krT [W/mm2] (2)
Convection boundary conditions are assigned for all free surfaces. The internal heat generation
rate by the welding torch, modeled with a double ellipsoid heat source model [23], is given as,
Q =6
3Qb()f
abc
e[
3x2
a2+ 3y
2
b2+ 3(
z+vt)2
c2] [W/mm3] (3)
where Qb is the welding heat input; is the welding efficiency, x, y, and z are the local coordinates of
the double ellipsoid model aligned with the weld fillet; a is the weld width; b is the weld penetration;
c = 4a is the weld ellipsoid length, and f = 0.6 when the torch is behind the analysis plane, and
f = 1.4 after the torch passes the analysis plane; v is the torch travel speed; and t is time. Material
properties for high-strength steel (HSLA-65) are used in this study. Table 1 lists the values of Qb,
and v that are used for the GMAW and SAW processes.
The subsequent history dependent stress analysis is performed by modelling the stress problem
as a quasi-static process in a Lagrangian frame. This problem has been covered by several
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investigators [6, 14, 5, 12, 10]. Similar to the heat transfer analysis, the numerical implementation
of the quasi-static analysis involves an incremental scheme with several small static increments. The
solution at a given time interval is obtained by using the solution at the previous time increment
as an initial condition.
The temperature values solved for in the previous thermal analysis are imported to the
mechanical analysis as loading. Generalized plane-strain conditions are assumed to account for
the out-of-plane expansion in the structure. The longitudinal (out-of-plane) strain is assumed to
vary linearly with x- and y- coordinates in the analysis plane:
z = e xy + yx (4)
where e is the z-component of the strain at the coordinate origin and the constants x and y
represent the strain variations in the y and x axes, respectively.
The stress equilibrium equation is given by,
r(r, t) + b(r, t) = 0 in Vr (5)
where is the stress, b the body force, and t is time. The mechanical constitutive law is :
= C ( p t) (6)
p = q a (, q, T) (7)
f = e y 0 (8)
where T is temperature, C is the material stiffness tensor, a is the plastic flow vector, , p and t
are the total, plastic and thermal strains and q is the equivalent plastic strain. In Equation 8, f
is the yield function, e is the Von Misses stress, and y is the yield stress. Active yielding occurs
when f = 0.
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Figure 4: FEA mesh for 2-D welding process analysis
2.3 Structural Analysis
In shipbuilding, stiffeners are joined to panels with fillet-welding along the free edge of the web,
thus, the straightness of this edge after the stiffener fabrication process is important for the quality
of the fit-up between the stiffener and the panel. The structural analysis is carried out for the
stiffener web to compute bowing distortions, and the critical welding residual stress that will cause
buckling.
The longitudinal residual stress distribution (r) computed in the 2-D analyses are compared
to the critical buckling stresses (cr) of the structure from the 3-D structural analysis to determine
if the structure will buckle.
The structural analysis is composed of elastic eigenvalue and linear stress analyses. Incremental
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Figure 5: FEA mesh for 3-D buckling analysis
large deformation analyses may also be performed to determine the onset of buckling, buckling and
post buckling stages in response to increasing stress, but they are computationally intensive and
are usually used for validating the predictive methodology [17].
3-D Eigenvalue Buckling Analysis:
The elastic instability problem is defined as an eigenvalue problem as follows
det ( K + KG ) = 0 (9)
where K and KG are the linear and non-linear strain stiffness matrices, and is the eigenvalue,
respectively.
A 3-D eigenvalue analysis is performed on the structural model with a unit negative thermal
load applied in the weld region (T = 1.0) to model the uniform compressive longitudinal plastic
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strain field occurring in welding. The eigenvalues (i) represent the multipliers (scaling factors)
which result in the critical buckling stress field (cr)i when multiplied with the stress field resulting
from the unit thermal load (L). Equation (10) shows the computation of the critical residual stress
distribution at the plate midspan.
(
cr)i = i
L [MPa] (10)
The scalar stress values L, cri and r, that are used in the buckling criteria, are computed at the
free edge of the stiffener web.
The buckling analyses may yield negative eigenvalues, which often cannot be explained by
physical behavior. Those situations can be avoided by applying enough preload Tp, to load the
structure just below the buckling load before performing the eigenvalue analysis. In such a case,
the critical buckling stress in equation (10) is determined as
(cr)i = ( i + | Tp | ) L [MPa] (11)
Buckling distortion is determined from the eigenvectors (mode shapes) of the structure. The
structure may buckle in any of the modes with critical stresses lower than the residual stress field
due to welding. It will prefer to buckle with the permissible buckling mode having the lowest
critical stress. The permissibility of the modes are determined by the constraints on the structure.
Certain buckling modes may be suppressed by the mechanical fixturing applied, then the structure
will tend to buckle the next available (higher) mode. The weight of the structure might have an
influence of causing even higher buckling modes.
3-D Linear Stress Analysis:
A 3-D linear stress analysis is performed using the negative unit thermal load applied in the
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weld region (T = 1.0). The bowing distortion, d, at the plate midspan for a given longitudinal
welding residual stress field (r) is obtained by scaling the unit bowing distortion, dL, and linear
longitudinal stress profile, L, as follows,
d = (r
L) dL [mm] (12)
2.4 Validation
The predictive buckling analysis approach presented in this work has been verified to be accurate
by several researchers [17, 24]. The results from the experimental tests involving thermo-couple,
blind-hole drilling and out-of-plane distortion measurements have been reported to be in close
agreement with the computational results.
3 Numerical Implementation
The stiffener is fabricated by joining two plates longitudinally in a T-joint configuration. Two
different stiffener geometries are considered, as illustrated in Figure 6 and Table 2. The fillet welds
of size 1/4 in. are performed on both sides with dual-torches by either gas metal arc (GMAW)
or submerged arc welding (SAW). The influence of weld sequence is evaluated for simultaneous
(3.5 offset torches) and sequential welding cases. In addition to the geometry, weld sequence, and
process parameters, the effects of fixturing and mechanical restraint are investigated as the case
studies given in Table 3.
The boundary conditions used to implement the fixturing effects are:
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Figure 6: Dimensions of the T-type fillet welded stiffener
BW [in] tW [in] 2BF [in] tF [in] l [ft]
Small Section 6.9375 1/8 4.5 5/16 20.0
Large Section 15.625 5/16 10.5 5/8 20.0
Table 2: Dimensions of Small and Large sections
Free boundary (As-weld) condition
Restrained boundary (Rammed down) condition
The free boundary condition analysis allows the stiffener to bend during welding. This is the
most typical fixturing used in welding and the stiffener bending manifests itself as bowing distortion
(see Figure 3). The fixed boundary condition is formulated to model the future mechanical
straightening of the stiffener to be welded on a panel.
The finite element solutions are performed by utilizing the ABAQUS software both for the 2-D
and 3-D models. The implementation details pertaining to those problems; the type of elements,
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boundary and loading conditions, are presented to allow convenient reproduction.
2-D Welding Simulation
The translating torch for the welding heat input is programmed using the user-subroutines. The
2-D finite element mesh used in the heat transfer analysis of the small section is illustrated in Figure
4. The model is made up of heat conduction, quadratic(8 node), quadrilateral elements(ABAQUS
DC2D8). The small section is composed of 716 quadrilateral elements and 2401 nodes, and the
large section is composed of 2256 quadrilateral elements and 7280 nodes.
The quasi-static mechanical problem, following the heat transfer analysis, is discretized into
a generalized plane strain finite element model, using ten node, quadratic, reduced integration,
quadrilateral elements(ABAQUS CGPE10R), with the mesh identical to that used for thermal
analysis.
To model the restriction of the supporting plate, the downward motion of the plates should
be restrained. This is implemented by placing two nonlinear dashpot elements (ABAQUS
DASHPOT1) at the two outermost nodes of the 2-D model, to exert high damping forces to resist
the downward motion. The dashpot damping coefficient is defined as a nonlinear function of the
y-displacement as follows,
c =
106 y < 0
0 y 0[Ns/mm] (13)
The rammed-down condition is implemented by fixing the x-axis rotation degree of freedom of
the generalized plane strain elements in the 2-D model.
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3-D Buckling and Linear Stress Analyses
The 3-D structural finite element models are developed using shell and truss elements. The
shell elements are representing the stiffener web and flange, and truss elements are representing the
weld joint along the crossing of the flanges and the web. The negative plastic strain resulting from
the weld process is applied to the truss elements in the form of negative thermal load. Trusses only
have axial degrees of freedom, thus, they will only experience orthotropic thermal expansion, and
the longitudinal compressive strains will accurately be modelled.
The model for small stiffener contains 8400 shell elements(ABAQUS S4R5), 350 truss
elements(ABAQUS T3D2), and a total of 8775 nodes; the large stiffener model has 18900 shell, 350
truss elements and 19305 nodes. The 3-D finite element mesh of the small stiffener is illustrated in
Figure 5. The use of structural elements rather than continuum elements is aimed at providing a
more robust design tool. With structural elements, geometric features such as the plate thickness
and the truss cross sectional area can be modified conveniently without changing the whole model.
For the free boundary condition case, the structural analysis, for both the small and large
sections, required a preload of Tp = - 0.05 be applied to the structure; whereas for the restrained
case, the reduced number of degrees of freedom eliminated the need to apply a preload (Tp = 0.0).
3.1 Results
The longitudinal residual stress distributions have come out to be as expected in both boundary
settings; for the as-weld configuration the regions close to the torch have tensile stresses, and the
areas away from the torch close to the flange edges, the stresses become compressive; only near the
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Case Weld Boundary Condition
1 GMAW (3.5in offset) free
2 GMAW (sequential) free
3 SAW (3.5in offset) free
4 SAW (sequential) free
5 GMAW (3.5in offset) restrained
6 GMAW (sequential) restrained
7 SAW (3.5in offset) restrained
8 SAW (sequential) restrained
Table 3: Weld Cases
free span of the web they become tensile to equilibrate the stress field in the web. Stress profiles
remain the same for the restrained boundary, except that the areas close to web free span now have
compressive stresses due to the fixed displacement conditions. The residual stress distributions
along the centre line of the stiffener web for the free and rammed-down cases are shown in Figure
7 to illustrate the influence of the boundary conditions.
The analysis was repeated for the 2-D welding simulation of the SAW process with the same
boundary conditions and the welding schemes. The results are compatible to those of GMAW
process and they have been tabulated in Tables 4 and 5 for small section; and Tables 7 and 8 for
large section.
3.1.1 Buckling in Small Stiffener
Tables 4 and 5 give the critical and residual longitudinal stress values required for buckling
prediction, as well as the bowing and angular distortions occurring in the eight different weld
cases. Table 6 presents the eigenvalues for the first 10 buckling modes obtained from the 3-D
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Case Weld Angular distortion Bowing distortion Residual Stress Critical Stress Buckling
1 (deg) 2 (deg) d (mm) r [MPa] cr [MPa]
1 GMAW (3.5in offset) 89.290 89.462 42.948 79.876 458.90 No
2 GMAW (sequential) 89.572 89.212 28.839 58.248 458.90 No
3 SAW (3.5in offset) 88.835 89.466 46.219 93.378 458.90 No
4 SAW (sequential) 89.290 89.021 33.804 68.275 458.90 No
Table 4: Results for the Free Boundary Condition cases for Small Section
Case Weld Angular distortion Bowing distortion Residual Stress Critical Stress Buckling
1 (deg) 2 (deg) d (mm) r [MPa] cr [MPa]
5 GMAW (3.5in offset) 89.262 89.448 0.0 -168.309 -71.40 Yes
6 GMAW (sequential) 89.590 89.156 0.0 -123.512 -71.40 Yes
7 SAW (3.5in offset) 88.838 89.436 0.0 -205.709 -71.40 Yes
8 SAW (sequential) 89.284 88.983 0.0 -146.997 -71.40 Yes
Table 5: Results for the Restrained Boundary Condition cases for Small Section
buckling analysis.
Free Boundary (As-weld) Condition
The critical stress (cr) in Table 4 corresponds to the first eigenvalue. Figures 8 and 9 illustrate
the residual stress distribution for the 3.5 offset and sequenced GMAW processes with free
boundary conditions, respectively. A possible mode of buckling for the as weld case is shown
in Figures 10. As listed in Table 4, in none of the cases, does the longitudinal stress at the edge
of the web exceed the critical stress value (458.90 MPa), thus, this condition will not cause any
buckling.
Restrained Boundary (Rammed-down) Condition
The residual stress values (-123.51 to -205.71 MPa) in the welding cases considered are greater
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Boundary Condition L (MPa) dL (mm) i
Free 6541.72 3238.90 0.020149
(Tp = - 0.05) 0.020149
0.020396
0.020399
0.020477
0.020483
0.020612
0.020614
0.020782
0.020803
Restrained -12184.75 0.0 0.000896
(Tp = 0.0) 0.003532
- 0.00553
0.005660
0.005663
0.005698
0.005708
0.005760
0.005788
0.005860
Table 6: 3-D Buckling Analysis Results of the Small Stiffener
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Case Weld Angular distortion Bowing distortion Residual Stress Critical Stress Buckling
1 (deg) 2 (deg) d (mm) r [MPa] cr [MPa]
1 GMAW (3.5in offset) 89.95 89.70 3.796 19.950 528.844 No
2 GMAW (sequential) 90.00 89.73 1.990 10.455 528.844 No
3 SAW (3.5in offset) 89.84 89.68 5.173 27.191 528.844 No
4 SAW (sequential) 89.94 89.70 2.604 13.688 528.844 No
Table 7: Results for the Free Boundary Condition cases for Large section
Case Weld Angular distortion Bowing distortion Residual Stress Critical Stress Buckling
1 (deg) 2 (deg) d (mm) r [MPa] cr [MPa]
5 GMAW (3.5in offset) 89.95 89.70 0.0 -34.531 -13.244 Yes
6 GMAW (sequential) 90.00 89.73 0.0 -19.421 -13.244 Yes
7 SAW (3.5in offset) 89.83 89.68 0.0 -45.797 -13.244 Yes
8 SAW (sequential) 89.94 89.69 0.0 -25.337 -13.244 Yes
Table 8: Results for the Restrained Boundary Condition cases for Large Section
than the critical stress of the restrained small stiffener (-71.40 MPa)(see Table 5). The critical
stress corresponds to the 10th eigenmode of the structure. This condition will result in buckling
distortions with a probability of buckling in a mode higher than the 10th eigenmode.
Figures 11 and 12 are the residual stress distributions for the simultaneous and sequenced
GMAW processes, respectively. The 4th and 10th eigenmodes for the rammed-down case are given
in Figures 13 and 14, to illustrate possible buckling modes. The higher modes have the same
characteristic shape due to the closely spaced eigenvalues, and the stiffener may buckle in any of
those shapes depending on the mechanical restraints.
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Boundary Condition L (MPa) dL (mm) eigenmodes
mode eigenvalue ()
Free 4946.17 47.05 1 0.05692
(Tp = - 0.05) 2 0.057013
3 0.0574
4 0.057873
5 0.058315
6 0.059409
7 0.059976
8 0.060931
9 0.062619
10 0.06343
Restrained -7407.27 0.0 1 0.001788
(Tp = 0.0) 2 0.007010
3 0.011079
4 0.011119
5 0.011367
6 0.01167
7 0.012006
8 0.012395
9 0.01288
10 0.01337
Table 9: Results for the 3-D Buckling Analysis of the Large Stiffener
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3.1.2 Buckling in Large Stiffener
Similar to small stiffener results, Tables 7 and 8 summarize the welding simulation, linear stress
and buckling analysis results.
Free Boundary (As-weld) Condition
The longitudinal residual stress distributions for the 3.5 offset and sequenced GMAW processes
are plotted in Figures 15 and 16, respectively. The first critical stress value (528.84 MPa) for the
as-weld large stiffener structure, corresponding to the first eigenvalue (0.05692) in Table 9, is an
order of magnitude higher than the residual stress values(10.46 to 27.19 MPa) for the four cases
(Table 7), which indicates that the structure in this configuration will resist buckling. A possible
mode of the free large stiffener is given in Figure 17.
Restrained Boundary (Rammed-down) Condition
Figures 18 and 19 are the residual stress values for the two welding sequences. For all four
welding cases, ramming-down will result in buckling distortions, since the residual stresses (Table
8) are higher than the critical stress (-13.24MPa). Moreover, the residual stress values for those cases
fall between the first and second critical stresses (-13.24MPa and -51.92MPa), thus the stiffener is
predicted to buckle in its 1st eigenmode shown in Figure 20 with the restrained boundary condition.
The weight of the structure may have an effect of causing a higher buckling mode, such as the one
given in Figure 21 (3rd mode).
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4 Conclusions
This paper has presented a numerical analysis technique to predict the welding-induced distortion
in fabricated stiffeners. In particular, angular, bowing, and buckling distortion were evaluated
using thermo-mechanical and eigenvalue finite element analyses. The following conclusions can be
drawn based on the results obtained,
Moderate angular distortions are predicted for all cases. The angular distortions computed
for GMAW and SAW are equivalent.
For the small section geometry, bowing is large in magnitude (28.8 to 46.2mm, in Table 4). It
is considerably reduced in the large stiffener (2.0 to 5.2 mm, in Table 7), and can be ignored
in the scope of many applications.
Sequenced welds lead to reduced distortion and residual stresses (Reductions from 46.2mm
to 33.8mm, and 93.38MPa to 68.28MPa), and possibility of buckling, in turn, is also reduced.
Although it may cause large bowing distortion, the as-weld condition did not cause any
buckling distortion for both stiffeners.
Buckling is predicted to occur when the stiffener is pressed (rammed) down on a straight
panel for future welding. As a consequence of straightening the web edge to correct the
bowing distortion, buckling becomes inevitable in both the small and large stiffeners. The
buckling pattern introduced particularly in the restrained small stiffener case (Figure 13), is
detrimental, and will make the future welds difficult to track along the distorted web.
Employing large section rather than small cross section stiffener reduces the bowing distortion
and the probability of buckling by enhancing the structural rigidity. The residual stress values
are lower and the critical stresses are higher than those of the small section, both of which
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are in favor of reducing the susceptibility to buckling. The buckling pattern of the restrained
case for the large section as illustrated in the Figure 20 is also more tolerable than that of
the small section (Figure 14.
Figure 7: Residual Stress Distribution along the centerline (small stiffener)
4.1 Recommendations
Manufacturing process modifications can be utilized to minimize bowing distortion. Conventional
techniques such as reducing the welding heat input, weld size, or modifying the structural
parameters, might be employed to eliminate the occurrance of buckling [25, 26, 27]. When the design
considerations dont permit such modifications, welding-distortions are remedied by utilizing special
manufacturing procedures during the fabrication process, such as thermal tensioning [28, 29, 30].
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Auxiliary heating may also be applied to minimize the residual stresses; that will enable the
application of restrained boundary conditions to eliminate the bowing distortion without causing
any buckling.
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Figure 8: Residual stress for the as-weld small section zz (MPa) for case 1 (20X magnification)
Figure 9: Residual stress for the as-weld small sectionzz (MPa) for case 2 (20X magnification)
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Figure 10: Buckling mode of free small stiffener (3rd mode)
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Figure 11: Residual stress for the rammed-down small section zz (MPa) for case 5 (20X
magnification)
Figure 12: Residual stress for the rammed-down small sectionzz (MPa) for case 6 (20X
magnification)
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Figure 13: Buckling mode of rammed-down small stiffener (4th mode)
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Figure 14: Highest buckling mode of rammed-down small stiffener (10th mode)
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Figure 15: Residual stress for the as-weld large section zz (MPa) for case 1 (50X magnification)
Figure 16: Residual stress for the as-weld large section zz (MPa) for case 2 (50X magnification)
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Figure 17: Buckling mode of the free large stiffener (1st mode)
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Figure 18: Residual stress for the rammed-down large section zz (MPa) for case 5 (50X
magnification)
Figure 19: Residual stress for the rammed-down large section zz (MPa) for case 6 (50X
magnification)
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Figure 20: Buckling mode of the rammed-down large stiffener (1st mode)
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Figure 21: Highest buckling mode of rammed-down large stiffener (10th mode)
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