Download Effects of temperature-dependent material properties on welding

Computers and Structures 80 (2002) 967–976
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Effects of temperature-dependent material properties
on welding simulation
X.K. Zhu, Y.J. Chao
*
Department of Mechanical Engineering, University of South Carolina, Columbia, SC 29208, USA
Received 22 August 2001; accepted 11 January 2002
Abstract
Detailed three-dimensional nonlinear thermal and thermo-mechanical analyses are carried out using the finite element welding simulation code––WELDSIM [Chao et al., In: Advances in Computational & Engineering Science, vol.
II, Tech Science Press: Paledale, USA: 2000. pp. 1206–1211]. The objective is to investigate the effect of each temperature-dependent material property on the transient temperature, residual stress and distortion in computational
simulation of welding process. Welding of an aluminum plate using three sets of material properties, namely, properties
that are functions of temperature, room temperature values, and average values over the entire temperature history in
welding, are considered in the simulation.
Results show that (a) the thermal conductivity has certain effect on the distribution of transient temperature fields
during welding, (b) the yield stress and Young’s Modulus have significant and small effects, respectively, on the residual
stress and distortion, after welding, and (c) except for the yield stress, using material properties at the room temperature
gives reasonable predictions for the transient temperature fields, residual stress and distortion. Since high temperature
material properties are either difficult to obtain or do not exist for many materials, an engineering approach is proposed
based on the results in this study. The engineering approach suggests using simplified properties constituted by a piecewise linear function with temperature for the yield stress and constant room-temperature values of all other properties
for computational weld simulation. Ó 2002 Elsevier Science Ltd. All rights reserved.
Keywords: Welding simulation; Material property; Residual stress; Welding distortion; Thermal modeling; Three dimension; Finite
element analysis
1. Introduction
Many metallic structures in industry are assembled
through some kind of welding process which is composed of heating, melting and solidification using a heat
source such as arc, laser, torch or electron beam. The
highly localized transient heat and strongly nonlinear
temperature fields in both heating and cooling processes
cause nonuniform thermal expansion and contraction,
and thus result in plastic deformation in the weld and
surrounding areas. As a result, residual stress, strain and
*
Corresponding author. Fax: +1-803-777-0106.
E-mail address: [email protected] (Y.J. Chao).
distortion are permanently produced in the welded
structures. High tensile residual stresses are known to
promote fracture and fatigue, while compressive residual
stresses may induce undesired, and often unpredictable,
global or local buckling during or after the welding. It is
particularly evident with large and thin panels, as used
in the construction of automobile bodies and ships.
These adversely affect the fabrication, assembly, and
service life of the structures. Therefore, prediction and
control of residual stresses and distortion from the
welding process are extremely important in the shipbuilding and automotive industry.
Over the past 20 years, research has been conducted
enabling the use of advanced analytical procedures to
more accurately simulate the welding process. Due to
0045-7949/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved.
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X.K. Zhu, Y.J. Chao / Computers and Structures 80 (2002) 967–976
the complexity of the physical processes involved in
welding, however, simple mathematical solutions cannot
address the practical manufacturing processes. Furthermore, it is also impossible for any experimental
technique to obtain a complete mapping of the residual
stress and distortion distribution in a general welded
structure. Computational simulation thus plays an indispensable role in the integrity analysis of such welded
structures. Hibbitt and Marcal [8] marked the first step
in applying a two-dimensional (2D) finite element
analysis (FEA) to predict residual stresses in a weldment. Due to computational and cost limitations, FEA
simulation efforts during the 70s and 80s were focused
on simplified 2D geometries [9,14]. In reality, the thermal and stress–strain responses of all weldments are
three-dimensional (3D). With recent advancements in
computational power, FEA simulation of transient
temperature and residual stresses in welding has gradually become feasible. Recently, 3D welding simulation
was conducted using commercial FEA software, as reported by Tekriwal and [18,19], Brown and Song [1],
Michaleris and DeBiccari [15], Dong et al. [6], and Chao
et al. [4].
In a computational simulation of welding process,
material modeling is one of the key problems. Recently,
Lindgren [10] gives a detailed review on this topic, which
includes the development of material constitutive relationships, material microstructures and material properties as functions of temperature. Most publications in
welding simulation adapted material properties that are
dependent on temperature. However, in practice complete temperature-dependent material property data required for welding simulation are difficult to obtain,
especially at high temperatures. To circumvent this
problem, assumptions and simplifications are often
proposed for welding simulation. Stanley and Chau
[17] first explored effects of the temperature-dependent
properties on thermal stresses in cylinders. Free and
Goff [7] assumed all material properties (except the yield
stress) remaining as the room temperature values to
model welding. Canas et al. [2] studies the influence of
strain hardening and temperature-dependent properties
on the residual stresses. Ma et al. [13] simulated residual
stresses using constant material density, Poisson ratio
and thermal expansion coefficient. Little and Kamtekar
[12] and Little et al. [11] presented the effect of various
thermal properties and weld efficiency on transient
temperature during welding. Chen et al. [5] and Shi et al.
[16] numerically studied the effect of material properties
on the welding simulation using extrapolated material
properties at high temperature and using different fictitious data of material properties at high temperature
covering a bandwidth which includes the extrapolated
unknown data, respectively. These authors then concluded that the unavailable material property data at
high temperature have almost no effects on the residual
stresses and distortion. To reduce computational time,
many numerical analyses often used a cut-off temperature above which no changes in the mechanical properties are accounted for. Tekriwal and Mazumder [19]
showed that the residual stresses from FEA have small
changes for carbon steels when the cut-off temperature
varied from 600 to 900 °C, but the computational time is
significantly different.
Although various assumptions and simplifications
were applied in welding simulation, as cited in the
previous paragraph, the potential errors from these assumptions and simplifications to the transient temperature fields, residual stress and distortion are not assessed
and are uncertain [16]. To this end, the present paper
systematically investigates the errors associated with
each of the material properties in a welding simulation.
We performed detailed 3D thermal and thermomechanical welding simulations for a 5052-H32 aluminum alloy by using three sets of material properties, i.e.
those at the room temperature, averaged over the temperature history in the welding process, and as functions
of temperature. WELDSIM, a 3D FEA software developed at the University of South Carolina by the authors, is used [4] in the simulation. By comparing the
results for the three cases, the effect of each temperaturedependent material property on transient temperature,
residual stress and distortion is investigated.
Since high temperature material properties are either
difficult to obtain or do not exist for many materials, an
engineering approach is proposed based on the results in
this study. The engineering approach suggests using
simplified properties constituted by a piece-wise linear
function with temperature for the yield stress and constant room-temperature values of all other properties for
computational weld simulation. It is shown that this
approach yields transient temperature fields, residual
stress and distortion with sufficient accuracy, yet circumvents the difficulty in finding and using exact high
temperature material properties.
2. Geometry and computational simulation
2.1. Geometry configuration
For convenience, the classical gas metal arc welding
(GMAW) experiment by Masubuchi [14] is modeled in
the present welding simulation. Fig. 1 shows the geometry and welding configuration of the problem under
consideration. As shown in the figure, the moving torch
is applied on the longitudinal upper edge of the plate of
1220 mm long, 152.4 mm wide and 12.5 mm thick. The
plate is simply supported at both ends. Such a geometry
and arrangement are chosen to produce a complete set
of experimental data that include transient temperature,
X.K. Zhu, Y.J. Chao / Computers and Structures 80 (2002) 967–976
Fig. 1. Configuration of the welding plate (dimensions are in
millimeter).
residual stress, and distortion at various locations in the
plate. As such, it provides excellent information to validate results from any computer simulation.
The material used in the welding was 5052-H32
aluminum alloy. Thermal and mechanical properties of
the material are shown in Fig. 2(a) and (b), respectively. Detailed experimental setup and procedures can
be found in Masubuchi [14]. Six single-direction strain
gages were used for measuring longitudinal strains. Four
thermocouples were also mounted on the plate at dis-
969
tances of 12.7, 38.1, 76.2 and 144.8 mm from the top, as
shown in Fig. 1, to record the temperature history. A
dial gage was used to measure the transient deflection of
the beam at the lower, midpoint of the beam during
welding. After welding was completed and the plate
cooled to the room temperature, the longitudinal residual stresses along the middle section were determined
using rosette strain gages by sectioning the plate. The arc
traveling speed is 7.34 mm/s which yields a 166 s total
time of welding. The welding current is 260 A, and the
arc voltage is 23 V. A Gaussian distribution with an
effective arc radius of 6 mm and thermal efficiency of
64.3% are used in the current computer simulation for
the heat flux applied to the plate.
2.2. Computational simulation
A half model in the thickness direction was used in
the computer simulation due to symmetry of the plate.
One layer of element is used in the FEA model, which
consists of 900 eight-node brick solid elements and 2020
nodes in both the heat transfer and the thermomechanical analyses. The smallest element used in the
modeling is in the area of the weld and has the dimensions of 12:2 mm 6 mm 6:25 mm. The finite element mesh is the same as that shown in Fig. 2 of Chao
et al. [4] and yields results with sufficient accuracy. It
should be mentioned that in a mesh sensitivity study [4]
a finer FEA mesh with 1800 elements and 3030 nodes
leads to almost identical results as the present FEA
mesh, but the computational time increased significantly.
An uncoupled thermal and thermo-mechanical analysis is adapted in this calculation. The thermal analysis
was performed first and the transient temperature outputs from this analysis are saved for the subsequent
thermo-mechanical analysis. In the thermal analysis, the
transient temperature field T is a function of time t and
the spatial coordinates ðx; y; zÞ, and is determined by the
3D nonlinear heat transfer equation:
kT;ii þ Qint ¼ cqT_
ð1Þ
where k is the conductivity, Qint is the internal heat
source rate, c is the specific heat and q is the density of
materials. The comma (,) denotes partial differentiation
with respect to a spatial coordinate, the dot (Þ denotes
differentiation with respect to time t. Heat flux to the
system is input by a moving source on the boundary. To
consider heat convection and radiation on the plate
surfaces, the heat flux loss is evaluated by
qs ¼ bðT T0 Þ þ eBðT 4 T04 Þ
Fig. 2. Variation of material properties with temperature of
5052-H32 aluminum alloy (a) thermal properties, (b) mechanical properties.
ð2Þ
where T0 is the room temperature, b is the convection
coefficient, e is the emissivity of the plate surfaces and
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B ¼ 5:67 1012 W=cm2 °C is the Stefan–Boltzmann
constant. In this calculation for the aluminum alloy,
b ¼ 30 W=m2 °C and e ¼ 0:03. In addition, a latent heat
of fusion is taken as 400 J/g to consider the phase
transformation of the aluminum.
In the thermo-mechanical analysis, the plastic deformation of materials is assumed to obey the Mises
yield criterion and the associated flow rule. The rate
relationship between thermal stresses, rij , and strains, eij ,
is described by
e_ij ¼
1þm
m
oa
r_ ij r_ kk dij þ ksij þ a þ
ðT T0 Þ T_
E
E
oT
ð3Þ
where E is Young’s modulus, m is Poisson ratio, a is the
thermal expansion coefficient. sij ¼ rij ð1=3rkk dij Þ are
the components of deviatoric stresses and k is the plastic
flow factor. k ¼ 0 for elastic deformation or re < rs , and
k > 0 for plastic deformation or re P rs , here rs is the
yield stress and re ¼ ð3=2sij sij Þ1=2 is the Mises effective
stress. A cut-off temperature of 400 °C (i.e. about 2=3 of
the aluminum melting temperature 607 °C) is used in the
numerical calculations to reduce unnecessary computational time. All FEA computations are performed on
PCs by using WELDSIM [4]. To save computational
time without loss accuracy of results, different time steps
are used for the two analyses. The time step used in this
study is 0.1 s for the heat transfer analysis, and 1.0 s for
the stress-deformation analysis. As such, the CPU time
in a typical welding simulation is about 1.2 min for the
temperature computation, and 81.8 min for the stress
and deformation computation.
2.3. WELDSIM––a WELDing SIMulation code
WELDSIM is a computer simulation software, developed at the University of South Carolina. The overall
structure of this software can be found in Chao et al. [4]
and Chao and Qi [3]. WELDSIM is a 3D, nonlinear
finite element computer code for the determination of
transient, as well as residual, temperature, stress, strain
and distortion of welded structures in a welding process.
Advanced features in the FEA code make WELDSIM
robust and computationally efficient. Its efficiency has
been verified through comparisons of computed results
with experimental data (see [3,4]).
In general, in WELDSIM, a heat transfer analysis
and a subsequent thermo-mechanical analysis can be
run sequentially or in a sequentially coupled manner. A
moving heat source simulating the torch is modeled first
to generate the temperature fields in the structure at
various time steps during the welding process, and then
the temperature history is used for the calculation of
thermal stress and displacement fields in the structure
during and after the welding process. The finite element
formulation and solver in WELDSIM follow the standard procedures in computational mechanics. Details
can be found in Chao and Qi [3]. Unique features in
welding implemented into the code include: moving heat
source model, complex heat input models for various
types of heat sources, latent heat for simulating melting,
dummy elements for simulating multi-pass welding, cutoff temperature to increase the computation speed, effective weight factor for elastic to plastic transition,
flexibility in convergence criterion for both the heat
transfer and stress analyses, both small and large deformation options for predicting distortion, and effect of
welding fixture to the residual stress and distortion.
3. Effect of thermal properties on temperature simulation
This section reports the numerical results of transient
temperature field for the three cases using the thermal
physical properties at room temperature, averaged over
temperature history and as functions of temperature. All
FEA results are compared with the experimental data
obtained by Masubuchi [14]. Accordingly, the effect of
various thermal properties on temperature simulation is
revealed and discussed.
3.1. Thermal modeling
The heat transfer equation (1) clearly indicates that
the material density q, specific heat c and thermal conductivity k are three primary thermal physical properties
in the thermal analysis. To avoid interaction of these
parameters in the study, each parameter is taken as the
room temperature (RT) value, average value over
temperature history and the value as functions of temperature, respectively, in the FEA computation. For
comparison, eight test cases as follows are considered in
our thermal modeling:
T1––all three parameters q, c, and k are functions of
temperature, as shown in Fig. 2(a).
T2––density q at RT, q ¼ q0 ¼ 2:69 g/cm3 , c and k
are functions of temperature.
T3––averaged density q ¼ q ¼ 2:64 g/cm3 , c and k
are functions of temperature.
T4––specific heat c at RT, c ¼ c0 ¼ 0:94 J=g °C, q
and k are functions of temperature.
T5––averaged specific heat c ¼ c ¼ 1:07 J=g °C, q
and k are functions of temperature.
T6––conductivity k at RT, k ¼ k0 ¼ 1:67 W=cm °C, q
and c are functions of temperature.
T7––averaged conductivity k ¼ k ¼ 2:06 W=cm °C, q
and c are functions of temperature.
T8––all three parameters are taken as the RT values,
i.e. q ¼ q0 , c ¼ c0 and k ¼ k0 .
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Since all thermal properties are functions of temperature in Case T1, the FEA result of temperature is
referred to as the baseline or standard numerical solution. All other FEA results of temperature for Cases T2–
T8 will be compared to that from Case T1, as well as the
test data, to evaluate the accuracy and error of simulation results for each case.
3.2. Numerical results for temperature
Fig. 3 shows the transient temperature history for
various densities at four test points for the three cases
T1, T2 and T3. The four points are the locations of the
thermocouples at distances of 12.7, 38.1, 76.2 and 144.8
mm from the top of the beam, as shown in Fig. 1, and
named as #1, #2, #3 and #4, respectively, in Fig. 3. The
experimentally measured temperature values at these
points obtained by Masubuchi [14] are also plotted in
the figure. Fig. 3 shows that the FEA results for Cases
T1, T2 and T3 are identical to each other, and match
well with the test data. Therefore, it is concluded that a
constant material density value at room temperature can
be used in numerical simulation to obtain good temperature results.
Fig. 4 shows the influence of various specific heat on
the distribution of temperature at the four tested points
for cases T1, T4 and T5. It is seen that the FEA results
for Cases T1, T4 and T5 are close to each other with
very small differences, and match well with the test data.
Therefore, a constant specific heat value at room temperature can be used in numerical simulation to obtain
good temperature results.
Fig. 5 shows the distribution of temperature at the
four tested points for various thermal conductivities for
cases T1, T6 and T7. The data in Fig. 5 indicate that (a)
Fig. 4. Effect of specific heat on the transient temperature at
four points. Using specific heat at the room temperature (Case
T4), average value (Case T5) and function of temperature (Case
T1).
Fig. 5. Effect of thermal conductivity on the transient temperature at four points. Using thermal conductivity at the room
temperature (Case T6), average value (Case T7) and function of
temperature (Case T1).
Fig. 3. Effect of density on the transient temperature at four
points. Using density at the room temperature (Case T2), average value (Case T3), and function of temperature (Case T1).
the FEA results for the RT conductivity (Case T6)
overestimated the temperature relative to those from the
standard Case T1, with the maximum error less than
10%, and (b) the numerical results from using the averaged conductivity (Case T7) are nearly the same as
those obtained from the standard Case T1. Moreover,
all FEA results for Cases T1, T6 and T7 agree well with
the test data. Therefore, two conclusions can be made
here, (a) the averaged conductivity can be used to obtain
as good numerical prediction as using temperaturedependent conductivity, and (b) using a constant conductivity at room temperature can also give reasonable
approximation of transient temperature field.
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X.K. Zhu, Y.J. Chao / Computers and Structures 80 (2002) 967–976
In addition, when all three thermal properties are
taken as the room temperature values, i.e. Case T8, the
FEA results of the transient temperature fields at the
four test points are almost identical to those for Case T6,
as shown in Fig. 5. Hence, they are not reproduced here.
Comparing to the standard Case T1, the results from
Case T8 only show a less than 10% difference.
In conclusion, from our studies in thermal modeling
of welding all thermal properties can be simply taken as
the room temperature values to yield the numerical
temperature results with sufficient accuracy. This validate the assumption of constant thermal properties used
by Free and Goff [7] and Canas et al. [2] in their welding
simulations.
4. Effect of mechanical properties on deformation simulation
This section presents the numerical results of residual
stress and deformation fields for three sets of mechanical
properties, i.e. property values at the room temperature,
the average values over the temperature history and the
values as functions of temperature. All FEA results are
also compared with the experimental data obtained by
Masubuchi [14]. As such, the effect of various mechanical properties on the deformation simulation can be
evaluated.
D3––E ¼ EðT Þ, rs ¼ rs ðT Þ and a ¼ aðT Þ. Temperature field is obtained from Case T8, i.e. all thermal
properties are taken as the room temperature values.
D4––Young’s modulus at RT, E ¼ E0 ¼ 69:3 GPa,
rs ¼ rs ðT Þ and a ¼ aðT Þ.
D5––averaged Young’s modulus, E ¼ E ¼ 44:5 GPa,
rs ¼ rs ðT Þ and a ¼ aðT Þ.
D6––yield stress at RT, rs ¼ rs0 ¼ 193 MPa,
E ¼ EðT Þ and a ¼ aðT Þ.
D7––averaged yield stress, rs ¼ rs ¼ 77:6 MPa,
E ¼ EðT Þ and a ¼ aðT Þ.
D8––thermal expansion at RT, a ¼ a0 ¼ 22:73 lm=
m °C, E ¼ EðT Þ and rs ¼ rs ðT Þ.
D9––averaged thermal expansion, a ¼ a ¼ 25:35
lm=m °C, E ¼ EðT Þ and rs ¼ rs ðT Þ.
D10––RT values for E and a, E ¼ E0 , a ¼ a0 , and
rs ¼ rs ðT Þ.
Since all thermal and mechanical properties are
functions of temperature in Case D1, the FEA result of
residual stress and deformation is referred to as a standard numerical solution in the deformation simulation.
All other FEA results of residual stress and deformation
for Cases D2–D8 will be compared to that for the
standard Case D1 in order to evaluate the accuracy of
simulation results for each case.
4.2. Effect of thermal properties on the residual stress and
distortion
4.1. Deformation modeling
From the elastic–plastic constitutive Eq. (3), it is seen
that Young’s modulus E, the yield stress rs and thermal
expansion coefficient a are three primary mechanical
properties in the thermo-mechanical analysis. The other
two parameters, i.e. the Poisson ratio m and plastic
hardening modulus Et have been proved no effects on
deformation modeling, respectively, by Tekrival and
Mazumder [19] and Canas et al. [2]. Therefore, in our
current calculation, m ¼ 0:33 and Et ¼ 0 are assumed.
Parameters E, rs and a are taken as the room temperature (RT) value, average value over temperature history and the value as functions of temperature in FEA
modeling. For comparison, 10 cases of thermal properties are considered in our thermal modeling as follows
(notice that Cases D4–D10 use the temperature field
from Case T1)
D1––E ¼ EðT Þ, rs ¼ rs ðT Þ and a ¼ aðT Þ are functions of temperature, as shown in Fig. 2(b). Temperature field is obtained from Case T1, i.e. all thermal
properties are functions of temperature.
D2––E ¼ EðT Þ, rs ¼ rs ðT Þ and a ¼ aðT Þ. Temperature field is obtained from Case T7, i.e. the average
value of conductivity.
Fig. 6(a) shows the distributions of residual stress in
the longitudinal direction, rxx , along the middle section
of the beam for Cases D1, D2 and D3. Fig. 6(b) shows
the transient deflection of the lower midpoint of the
beam for the three cases. The experimental data of the
residual stress and transient deflection measured by
Masubuchi [14] are also plotted in the two figures. It
should be noted that all mechanical properties used in
these three cases are functions of temperature. The
objective of the comparison shown in Fig. 6 is to investigate the change of thermal properties on the deformation simulation.
Again, the FEA results of the residual stress and
transient deflection predicted by using the averaged
conductivity (i.e. Case D2) are almost the same as those
from the standard Case D1. Except in the area close to
the weld line, the residual stress distribution in other
areas predicted by using thermal properties at room
temperature (i.e. Case D3) is in good agreement with
those of Case D1, and the maximum error is <10%. The
transient deflections predicted by Case D3 also agree
with those of Case D1, and the maximum error is about
10%. All FEA results for the three cases match well with
the test data for both the residual stress and the transient
deflection. It may be concluded that the various thermal
X.K. Zhu, Y.J. Chao / Computers and Structures 80 (2002) 967–976
Fig. 6. Effect of thermal properties on deformation simulation.
Using averaged conductivity (Case D2), the room temperature
properties (Case D3) and functions of temperature for all
thermal properties (Case D1). (a) Residual stress along the
middle section of the beam, (b) transient deflection at the lower
mid-point of the beam.
properties studied have no significant effects on deformation simulation.
4.3. Effect of mechanical properties on the residual stress
and distortion
The distribution of the residual stress along the
middle section and the transient deflection at the lower
midpoint of the beam for Cases D1, D4 and D5 are
shown in Fig. 7(a) and (b), respectively. Both numerical
results are compared with the test data. The comparison
in Fig. 7 indicates that (a) using the room temperature
value of Young’s modulus (i.e. Case D4) yields numerical results almost as good as the standard Case D1 for
both the residual stress and the transient deflection, and
(b) the FEA results match well with the test data. The
difference for the residual stress is only in the weld region, and the maximum error is about 13%. On the other
hand, using the averaged Young’s modulus (i.e. Case
D5) predicts the deflection after welding, i.e. after 500 s,
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Fig. 7. Effect of Young’s modulus on deformation simulation.
Using room temperature value of Young’s modulus (Case D4),
average value (Case D5) and function of temperature (Case
D1). (a) Residual stress along the middle section of the beam,
(b) transient deflection at the lower mid-point of the beam.
with an error about 11% relative to the standard Case
D1, while the FEA residual stress from Case D5 significantly deviates from that of the standard Case D1.
The maximum error of residual stress for Cases D5
compared to the standard Case D1 is more than 40%. In
conclusion, Fig. 7 shows that the predicted results using
the room temperature value of Young’s modulus in a
welding simulation are acceptable.
Fig. 8(a) and (b) shows the distribution of the residual stress along the mid-section of the beam and the
transient deflection at the lower midpoint of the beam,
respectively, for Cases D1, D6 and D7. It is interesting
to see from Fig. 8(a) that using the room temperature
value of the yield stress, rs0 (i.e. Case D6), in the simulation predicts ZERO value of the residual stress as well
as the permanent deflection after welding. It is well
known that the residual stress in weldment is caused by
plastic strains in regions where high temperature occurs
during welding. However, the constant rs0 overestimates
the material yield ability, which actually reduces with
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X.K. Zhu, Y.J. Chao / Computers and Structures 80 (2002) 967–976
Fig. 8. Effect of yield stress on deformation simulation. Using
room temperature value of yield stress (Case D6), average value
(Case D7) and function of temperature (Case D1). (a) Residual
stress along the middle section of the beam, (b) transient deflection at the lower mid-point of the beam.
increasing temperature in the high temperature region,
so that only elastic strains, but no plastic strains, occur
in the weldment. This is clearly demonstrated by the
variation of the transient deflection for Case D6 as
shown in Fig. 8(b). The deflection has the same tendency
as the test data during the welding, but restores to zero
value after the welding is completed and the room
temperature is reached. When the yield stress is changed
to the average value, the numerical results for Case D7,
as shown in Fig. 8, have the same tendency as the test
data for both the residual stress and deflection. But there
exhibits a large difference between Cases D7 and D1.
Accordingly, the yield stress has to be considered as a
function of temperature to predict correct deformation
in welding simulation.
Fig. 9(a) and (b) compares the variations of the residual stress and deflection for Cases D1, D8 and D9.
There is nearly no difference between the three cases,
and all FEA results match well with the test data for
both the residual stress and transient deflection. It can
be concluded that the thermal expansion coefficient can
Fig. 9. Effect of thermal expansion coefficient on deformation
simulation. Using room temperature value of thermal expansion coefficient (Case D8), average value (Case D9) and function of temperature (Case D1). (a) Residual stress along the
middle section of the beam, (b) transient deflection at the lower
mid-point of the beam.
be simply taken as the room temperature value in
welding simulation.
4.4. An engineering approach using simplified properties
The analyses and comparison above revealed that all
thermal and mechanical properties, except for the yield
stress, can be simply taken as the room temperature
values in welding simulation to give the residual stress
and distortion with sufficient accuracy. The yield stress
has to be considered as a function of temperature in the
thermo-mechanical simulation. Since the yield stress at
high temperature for engineering alloy is often not
readily available for welding simulation, an engineering
approximation to this particular material property at
high temperatures is investigated and proposed here. It
is assumed that the yield stress for the material under
consideration takes the room temperature value when
X.K. Zhu, Y.J. Chao / Computers and Structures 80 (2002) 967–976
0 6 T 6 100 °C, 5% of the room temperature value when
T P T1 ¼ 2=3 of the melting temperature of the material,
and a linear function of temperature in between, i.e.
100 °C < T < T1 . Note that T1 is essentially the cut-off
temperature used widely in numerical simulation for
welding to account for the close-to-zero yield stress as
the melting temperature of the material is approached.
Five percent (other than zero) is chosen arbitrarily to
avoid any numerical difficulties. We have performed
numerical tests and it was found that the selection of five
percent as well as a precise cut-off temperature is not
sensitive to the final results.
For the 5052-H32 aluminum alloy, the melting temperature is 607 °C and thus T1 ¼ 400 °C. The assumed
temperature-dependent yield stress for the 5052-H32
aluminum alloy can then be expressed mathematically
by the following piece-wise linear function
8
< rs0 ¼ 193 MPa;
rs ¼ 5%rs0 þ 400T
95%rs0 ;
300
:
5%rs0 10 MPa;
975
0 6 T 6 100 °C
100 < T < 400 °C
T P 400 °C
ð4Þ
The variation of the yield stress in (4) with temperature
is plotted in Fig. 2(b) in dashed line.
The simplified yield stress in (4) and the room temperature values for all other properties constitute an
engineering approximation for material properties in
welding simulation. The residual stress and deflection
from FEA using this simplification are depicted in Fig.
10. It is observed that the residual stresses are in very
good agreement with the test data as well as the standard
FEA results of Case D1, except perhaps for the weld
area. The maximum error of the peak value of the residual stress is about 13% in the weld area. The computed
transient and permanent deflections also match well with
both the test data and the standard FEA results. The
maximum difference in deflection between Case D1 and
the engineering approach is <10%. These results indicate
that the proposed engineering approach using simplified
material properties is a simple, yet effective, way in
welding simulation for the aluminum alloy.
5. Concluding remarks
Fig. 10. Comparison of the engineering approach for deformation simulation. Using temperature-dependent yield stress
and room temperature properties for others (Case D10); all
properties are functions of temperature (Case D1); and the
engineering approach using approximate rs as in Eq. (4). (a)
Residual stress along the middle section of the beam, (b)
transient deflection at the lower mid-point of the beam.
To investigate the effects of temperature-dependent
material properties on transient temperature, residual
stress and distortion in computational simulation of a
welding process detailed 3D nonlinear thermal and
thermo-mechanical analyses are performed using FEA
method. Three sets of material property for the 5052H32 aluminum alloy are investigated, i.e. values at the
room temperature, average values over temperature
history, and functions of temperature. Numerical results
are compared between the three sets, as well as compared with the test data. The main results and conclusions are summarized as follows:
(1) The thermal conductivity has some effect on the
distribution of transient temperature field during welding. The material density and specific heat have negligible effect on the temperature field. Although using the
average values over the temperature history is better,
adopting room temperature values of all thermal properties in the welding simulation can predict reasonable
results for the transient temperature distribution.
(2) The yield stress is the key mechanical property in
welding simulation. Its value has significant effect on the
residual stress and distortion. If the room temperature
value of the yield stress is taken, the FEA computation
predicts zero residual stress and no permanent distortion
because only elastic strain, and no plastic strain, occurs
under this circumstance. The temperature dependency of
the yield stress must be considered in a welding process
simulation to obtain correct results.
976
X.K. Zhu, Y.J. Chao / Computers and Structures 80 (2002) 967–976
(3) Young’s modulus and the thermal expansion coefficient have small effects on the residual stress and
distortion, respectively, in welding deformation simulation. It is found that the numerical results obtained by
using the room temperature value of Young’s modulus
are much better than those using its average value over
temperature history.
(4) An engineering approach using simplified properties, constituted by a piece-wise linear function with
temperature of the yield stress and the constant room
temperature values of all other properties, is proposed
and validated for computational welding simulations of
aluminums. Similar approach can be extended to welding simulation for steels. The proposed simplification
methodology for material properties is most useful for
welding simulation when detailed material properties at
high temperatures are unavailable.
Acknowledgements
The authors wish to thank the support of this work
by the National Science Foundation through Grant
CMS0116238, program director Dr. K.P. Chong.
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