Analysis of Weld Puddle Distortion and Its Effect on Penetration

6 Pages·0.483 MB·English

by  Friedman Е.

Analysis of Weld Puddle Distortion
and Its Effect on Penetration
Weld puddle distortion contributes significantly to weld penetration
characteristics, and the control of puddle surface tension is essential
to the control of weld puddle shape change
and the enhancement of penetration
By E. FRIEDMAN
ABSTRACT. An analytical finite ele liquid material and fluid motion in the locally distorted by gravitational forces
ment heat transfer model for the gas puddle. These in turn are dictated by and arc pressure" as well as by fluid
tungsten-arc (GTA) welding process is conditions at the weldment bound flow induced by magnetic and con
developed to account for distortion of aries, which include heat input from vective forces in the puddle. The
the weld puddle due to pressure from the arc, surface energy losses to the magnitude of this local distortion is
the welding arc and gravitational environment and distortion of the most pronounced during the root pass
forces in the puddle. The model is weld puddle due to the force of the of a full penetration weld and results,
employed to assess the combined welding arc impinging on its surface, upon solidification, in the weld under
effects of heat flow in the weldment as well as by convective and magneto- bead.
and changes in the puddle shape on hydrodynamic interactions. In the present work, the molten
weld penetration. The relationship The welding thermal cycle has been puddle is considered to be acted upon
between puddle configuration and simulated numerically using finite dif simultaneously by distributions of heat
penetration has not previously been ference approximations' as well as input from the arc, pressure from the
studied from an analytical point of finite element methods of analysis for arc and gravitational forces in the
view. transient heat conduction.- ' ' The heat puddle. The effects of magnetic forces
conduction mechanism for stationary and convective motion are not ad
GTA welds was studied extensively in dressed in the current treatment. The
Introduction
an analysis and test program designed arc pressure and gravitational forces
Extensive experimental data exist on to assess the effects of both the magni result in the top surface of the puddle
the effects of such welding parameters tude and the distribution of heat input being depressed below its original
as arc current, arc gap, weld speed and from the arc and of surface energy level prior to melting. If full penetra
shielding gas on weld bead depth and losses on penetration, weld bead tion is achieved, the same forces cause
width for the CTA welding process. width and temperatures for stationary the bottom surface of the puddle to be
What has been lacking, however, is a GTA welds.1' The finite element proce depressed. Surface tension at inter
clear understanding of how these and dures previously discussed1 were em faces between the liquid puddle and
other variables interact to produce the ployed for the analytical part of this the gaseous atmosphere serves to
observed weld bead shapes. To help investigation. resist puddle distortion. For full pene
develop this understanding, a syste Implicit in all these efforts is the tration welds, the surface tension
matic effort has been undertaken to assumption that the molten weld supports the molten material and
establish an analytical model of heat puddle maintains a fixed shape as heat prevents burn-through.
transfer in the molten weld puddle from the welding arc is being applied. The analytical model of weld puddle
and the surrounding solid material, ll Distortion of the weld puddle or weld distortion considers a stationary arc
is the flow of heat in the weldment ment has not previously been consid heating the surface of a flat plate. The
that ultimately determines the extent ered in analyses of temperature tran existence of a stationary arc implies
of the puddle and, therefore, the sients and weld bead penetration and that the distributions of both heat and
configuration of the solidified weld shape. The weld puddle is, however, pressure acting on the weldment
bead. Hence, characterization and surface are axisymmetric, thus sim
study of the heat transfer phenome plifying the analysis. Extension of the
non provide a vital link in gaining an Paper presented at the AWS 59th Annual model to moving welds would result
improved comprehension of how Meeting held in New Orleans, Louisiana, in a non-axisymmetric puddle, which
weld penetration and shape can be during April 2-7, 1978. complicates the analysis procedure.
controlled. This extension is unwarranted at this
E. FRIEDMAN is a Fellow Engineer in Reac
Heat flow in a weldment for the tor Technology, Bettis Atomic Power Labo time since much information may be
GTA process is governed by the mech ratory, Westinghouse Electric Corporation, gathered on the effects of various
anisms of heat conduction in solid and West Mifflin, Pennsylvania. welding and material variables on
WELDING RESEARCH SUPPLEMENT I 161-s
weld bead penetration and distortion
1—i—i—i—r -i—i—r k—i—r
from calculations based on the simpler
stationary arc model.
The analytical model for weld pud
dle distortion is presented first, fol
lowed by the results of calculations
made to determine the effects of arc
pressure and puddle surface tension
on weld bead shape and penetration,
WELD PUDDLE
and on puddle distortion.
r-AXIS
Analytical Model
The analytical model is based on the
weld puddle deforming under the
action of pressure from the welding
arc and gravitational forces in the
puddle only at temperatures exceed
ing the melting point. For purposes of
calculating these local deformations
(as opposed to distortion resulting, for
LIQUID-SOLID INTERFACE
example, from shrinkage strains), ma
terial at temperature less than the
liquidus is taken to be rigid.
At any given time during which heat
is being applied by the stationary heat
source, a given volume of the weld 10
ment material may be in the molten r-AXIS (mm)
Fig. 1—Weld bead distortion as depicted by deformed finite element mesh
state. This volume may or may not
fully penetrate the thickness of the
weldment. Nevertheless, its shape is At any time step during which the weldment in which temperatures ex
axisymmetric with respect to the temperature at one or more nodes of ceed the melting point.
center of the axisymmetric heat the finite element mesh exceeds the The BESTRAN finite element sys
source. The molten puddle is acted specified liquidus temperature, the tem7 is used to make these computa
upon by axisymmetric distributions of motion of these nodes due to arc tions. The output of the temperature
thermal energy, arc pressure and gravi pressure and gravity forces is deter calculations is used to determine what
tational forces. The surface tension at mined. The nodes at temperatures less region of the weldment is in the mol
the interface of the weld puddle with than the melting point are completely ten state and therefore subject to
the surrounding atmosphere supports restrained from any motion. As illus distortion. The results of the distortion
the molten material and prevents trated in Fig. 1, the calculated nodal calculations are utilized to calculate
burn-through. Surface tension at the displacements are employed to update the distorted finite element mesh
liquid-solid interface (see Fig. 1) is the undistorted mesh geometry. The required for the next set of tempera
not considered in this model. resulting distorted mesh is used for ture calculations.
temperature calculations in the next
The new features added to an earlier
time step.
heat transfer model'' are:
Temperature Calculations
1. Simulation of pressure from the An outline of the required calcula
welding arc and gravitational forces in tions is as follows: The application of heat from the arc
the puddle. 1. Calculate nodal temperatures in to the workpiece and the distorted
2. Distortion of the puddle due to time increment. geometry used for temperature calcu
these forces. 2. If all nodal temperatures are less lations is discussed briefly. Detailed
3. Resistance to puddle shape than the melting point (liquidus), procedures for calculating welding
change by surface tension at puddle return to Step 1 for the next time temperatures have been described in
interfaces with atmosphere. increment. the literature.'
4. Heat transfer in the weldment as 3. If any nodal temperature exceeds The heat input from the welding arc
the puddle continually changes the melting point, calculate displace is applied as a radially symmetric
shape. ments of nodes in the puddle. normal distribution function:
4. Add displacements to unde-
Calculational Procedure formed grid coordinates to obtain q(r) = [3Q/(OT„8)] exp [-3(r/r„H
distorted mesh geometry.
The computational process, which is 5. Return to Step 1 for the next time (1)
incremental in time, is an outgrowth of increment using the distorted geome
the nonlinear transient finite element try. where q is the heat flux acting on the
heat conduction analysis previously 6. Continue until solution becomes weldment surface, Q is the strength of
carried out for stationary arc welds.'' unstable. (This occurs subsequent to the heat source (that is, the product of
Although heat from the arc is applied full penetration when the undersur- the arc current, voltage drop and arc
at a constant rate, diffusion of heat face sag becomes very large, indicating efficiency), r is the distance from the
through the weldment is a time- the onset of burn-through.) weld centerline (see Fig. 1), and rh is a
dependent phenomenon requiring In general, calculations during an dimensional parameter defining the
calculations at a number of time steps. increment of time involve: region in which 95% of the heat from
The present analysis procedure de 1. Determinations of temperatures the arc is deposited. Thus, Q and rh
viates from that used previously"' when throughout the weldment, and completely define the steady applica
weldment material melts. 2. Distortions in that part of the tion of heat from the stationary arc.
162-s I IUNE 1978
The heat supplied by the arc is conditions (dw/dr)|,,=„ = 0 and Arc Pressure
conducted through the weldment in w(b) = 0, the following is obtained for
its distorted configuration. Under the the deflection: The pressure applied by the arc to
the surface of the weldment is taken to
action of arc pressure and gravitational
forces, the r«ated surface of the weld w(r) = In (b/r) /•' (q/N) p dp be distributed as a radially symmetric
(3)
puddle in the vicinity of the weld -/," (q/N) In (p/r) pdp. normal distribution function, such
centerline is depressed below its origi that
nal elevation, as shown in Fig. 1. It is This equation is used to establish a p(r) = p„ exp [-3(r/rf)!] (6)
this depression that may significantly relationship between the restraining where p is the pressure acting on the
affect the penetration characteristics forces of the membrane and the surface, p0 is the maximum pressure at
of the weld. Since all calculations are membrane deflections at a discrete the weld centerline, r is the distance
carried out in increments of time, the number n, of location's (corresponding from the weld centerline, and r, is a
weld puddle distortion progresses in to finite element nodes) on the puddle dimensionless parameter defining the
discrete steps, rather than continuous- surface. The deflection w = w(ri) at a region in which 95% of the electro-
i
location defined by r = t due to a magnetically-induced arc force is ap
ly- tl
ring load P,, applied at a distance r,, plied.
from the center of the membrane, is p„ and r, completely define the pres
Distortion Calculations
found by letting the pressure distribu sure distribution from the stationary
Puddle distortions are computed by tion q(r) = [Pj/(27r Tj)] S(r — tj), where arc. This is analogous to the steady
specifying mechanical properties of S is the Dirac-delta function, and distribution of heat applied to the
the weldment to simulate the behavior i,j = 1,2 n (r,,i > r,). Substituting weldment—see equation (1).
of a nearly incompressible liquid with this expression into equation (3), the
Results of Analysis
negligible shear resistance. The com following linear flexibility equation is
pressibility of the puddle is taken to be obtained: Since the purpose of this work is to
that of water at 10 C or 50 F w, = Qj P„ (4) assess the effects of arc pressure, grav
(50 X 10"/atm). This is equivalent to a where ity forces, and surface tension on
bulk modulus K, of 2 GPa (290 ksi). C„ = ln(b/r.) j<i penetration, weld bead dimensions,
(5)
Since a perfectly incompressible = ln(b/r,) j > i. y and puddle distortion, all computa
material, corresponding to a Poisson's tions were made for a heat input of
ratio v of 0.5, would generate a singular Equation (4) is generalized in matrix fixed magnitude and distribution ap
stiffness matrix in the finite element notation by: plied to the center of a 50.8 mm (2 in.)
program (BESTRAN), a small parame {w} - [C] {P} , diameter, 6.35 mm (0.25 in.) thick
ter a, is introduced such that v = where the elements of the symmetric circular Alloy 600 plate. The thermal in
0.5 (1-a). Letting the elastic modulus flexibility matrix [C] are given by equa put parameters used are Q = 1000 W
E = 3Ka, the bulk modulus K = tion (5). and r„ = 3.81 mm (0.15 in.). The
E/[3(1-2v)J is independent of a. A numerical problem arises when magnitude of heat input is equivalent
Results of a test problem yielded the ring load is applied at the center of to an arc current of 125 A, voltage drop
reasonable solutions for a = 2 x 10" the membrane. In the limit, this is of 10 V, and arc efficiency of 0.8, which
(see Appendix). Although the behavior equivalent to an infinite pressure are consistent with parameters used
of the entire weldment is character applied at the center, which results in previously."
ized in this manner, those finite an infinite deflection at the center. The effects of arc pressure and grav
element nodes at temperatures less This problem is circumvented by ity forces on penetration and weld
than the melting point are constrained calculating the flexibility coefficient at bead dimensions are illustrated by
to have zero displacement. node j = 1(r, =0) by linear extrapola determining the growth of the weld
tion of the corresponding terms evalu puddle with time neglecting puddle
Surface Tension ated at r, and r,. distortion (i.e., neglecting arc pressure
The inverse of the flexibility matrix is and gravity forces or assuming very
Distortion of molten material under the membrane stiffness matrix [Kj. The large surface tension), and then com
the action of arc pressure and gravita constraint effect of puddle surface paring the results with those obtained
tional forces is inhibited by the surface tension is incorporated into the finite using representative puddle distortion
tension existing at the interface be element model as an equivalent elastic parameters. For this purpose, a reason
tween puddle and atmosphere. At a foundation with stiffness [K|. able estimate of the maximum arc
given time, there may exist one or two The surface tension simulation pro pressure is taken to be 100 mm H,0,6-9
of these interfaces, depending upon
cedure was verified by formulating or 1000 Pa (0.15 psi). The arc pressure
whether partial or full penetration has
stiffness matrices for a circular mem distribution parameter r, is taken to be
been attained. f
brane of unit radius. The membrane is 3.81 mm (0.15 in.) (this is consistent
Surface tension is simulated in the acted upon by a uniform pressure q„, with the limited number of measure
finite element model by a membrane which is discretized by a series of ring ments reported in the literature), and a
with uniform isotropic tension equal loads applied at a given number of surface tension of 1000 dynes/cm, or
to the surface tension N. Consider a equally spaced nodes. The numerical 1N/m (0.0057 lb/in.) is used.
circular membrane of radius b, sup solution for deflection at each node The results plotted in Fig. 2 show
ported around its edge and subject to was compared with the exact solution, that the distortion of the puddle
a normal pressure q(r), which may vary given by w(r) = q„ (I — r2)/(4N). Errors contributes significantly to the pene
radially. The normal deflection w, of of less than 0.4% were obtained with tration characteristics of the weld—es
the membrane satisfies the equilib 10 nodes used in the discretization. pecially when the depth of penetra
rium equation:' The use of more nodes reduces the
tion approaches the weldment thick
error. Problems run to assess the accu
ness. When including the effects of
(1/r) (d/dr) (r dw/dr) = -q/N, racy of the puddle distortion computa
puddle distortion due to arc pressure
tional procedure, which couples the
and gravity forces, full penetration
(2) effects of forces transmitted through
occurs after 32 s of heating; neglecting
molten metal and of surface tension,
provided d'-w/dr'- <<1. puddle distortion, full penetration is
are described in the Appendix.
Integrating this equation with the not yet attained at 40 s.
WELDING RESEARCH SUPPLEMENT I 163-s
1 1 I 1 1 1 1 1 1 1 |
P0•1500 Pa
P0 • 1000 Pa
P0 =500 PO
'£~-""~ WIDTH AT TOP SURFACE
FULL PENETRATION / ^
^ *AAT7~~~/ / WIDTH AT /
~T''~' / A BOTTOM S ~.
/ 7 / / SURFACE' / '' *'
JT DEPTH OF PENETRATION
7 /
1 ( if "
Fig. 2—Effect of puddle distortion on puddle dimensions. Maximum Fig. 3—Effect ot arc pressure on puddle dimensions. Maximum arc
pressure = 1000 Pa (0.15 psi); surface tension = 1 N/m (0.0057 pressure - p„; surface tension =1 I 1N /m1 (01 .0015 71 lb/in.)
lb/in.)
2.5
1000
MAXIMUM ARC PRESSURE(Pd)
Fig. 4—Effect of arc pressure on time to lull
penetration. Surface tension = I N/m
(0.0057 lb/in.)
The maximum arc pressure resulting
from electromagnetic forces is propor
tional to the square of the current." It is
thus of interest to determine the
effects of arc pressure on the growth
and penetration of the weld puddle.
(Although an increase in current
produces increases in both heat input
and arc pressure, only the latter is
considered here. The effects of heat
input on penetration and weld bead
shape are found elsewhere.')
The results are presented in Fig. 3,
in which the growth of the puddle
dimensions with time are plotted for a
number of values of the maximum arc
pressure. Additional information ap
pears in Fig. 4, which shows how the
time to full penetration is influenced
by the magnitude of the arc pressure.
Figure 3 also demonstrates that arc
pressure significantly influences weld 0 IOOO 2000
penetration when the puddle pene MAXIMUM ARC PRESSURE (Pa)
trates to approximately 60% of the fig. 5—Weld puddle distortion as a lune tion of arc pressure for various durations
weldment thickness. of heating. Duration of heating = t*; surface tension = I N/m (0.0057 lb/in.)
For these penetrations, the depres
sion of the heated surface of the the rate of further penetration de the surface is depressed. The effect on
puddle is of sufficient magnitude that pends strongly on the degree to which bead width (at the heated (top)
164-s I JUNE 1978
i i 1 1 I II r T—i
- 1 N/m
N = 0.5 N/ ^-H-"" ___
10 = 0.1 N/
N
^
WIDTH AT TOP SURFACE
f 8
e
z * /y
o
- '/ FULL PENETRATION /
S 6 1/ / l^
a
-ai y ^7
H 4 ^
.'WIDTH AT BOTTOM S
DEPTH OF / SURFACE y^
PENETRATION 1 / _
2 1 ,
Y * NUMERICAL SOLUTION / /
j BECOMES ILL-BEHAVED
1 i 1 I i 1 i I I i li I i 1 !
Fig. 6—Effect of surface tension on puddle dimensions. Surface
tension = N; maximum arc pressure = 7000 Pa (0.15 psi)
0.5 -
Fig. 7—Top surface puddle depression as a function ol surface
tension for various durations of heating. Duration of heating = t*;
maximum arc pressure = 7000 Pa (0.15 psi) 0.5 I.O
SURFACE TENSION (N/m)
surface) is less pronounced, since the volume that results from pressure- 0.5<N<1.0 and a rather shallow
influence of puddle depression on the induced puddle distortion brings puddle (exposure times of 1.6 and 13
radial transfer of heat in the weldment about a greater degree of distortion. s), the depression of the puddle is
is less than on the heat transfer An increase in arc pressure, there inversely proportional to the surface
through the thickness. fore, produces both an increase in tension.
Arc pressure enhances penetration puddle distortion and an increased For higher exposure times (e.g., 26
because of its ability to depress the puddle volume. The latter, in turn, s), enhanced puddle depression results
molten weld puddle, thus resulting in effects a further increase in puddle in energy from the arc being applied at
thermal energy from the arc applied at distortion, thus causing the deviation a level sufficiently below that of the
a level below that of the undistorted from linearity of the top surface undistorted weldment that the depth
weldment surface. The shape of the puddle depression shown in Fig. 5. For of penetration and volume of the
distorted puddle is, however, of inter sufficiently high magnitudes of puddle puddle are significantly greater than
est in its own right, since it contributes distortion (subsequent to full penetra they would be if the puddle were not
to the configuration of the solidified tion), the rates of increase of puddle depressed. Thus, a decrease in surface
weld bead. This is an especially impor depression at both top and bottom tension causes increases in both pud
tant effect for full penetration welds, surfaces are very sensitive to increases dle depression and volume, with the
as illustrated in Fig. 1. The variation of in pressure. latter effecting a further increase in
the magnitude of puddle depression at The final parameter study performed depression, as explained previously.
the weld centerline with arc pressure was on the influence of surface This phenomenon yields the more
is shown in Fig. 5. Here the maximum tension on puddle dimensions and pronounced effect of surface tension
depression of the puddle at both the puddle distortion. Calculations were on puddle depression that is observed
top and, for full penetration welds, made for values of surface tension in Fig. 7 for a heating time of 26 s.
bottom surfaces are plotted against N = 1,0.5, and 0.1 N/m (0.0057,0.0029, For values of surface tension much
pressure at the weld centerline for a and 0.0006 lb/in.) to illustrate the higher than 1 N/m (0.0057 lb/in.), the
number of durations of heating. sensitivity of this physical property. restraint effect becomes very large and
If the magnitude of weld depression Figure 6 shows the effect of surface the limiting case of no distortion is
at the top surface is less than 10% of tension on penetration when the approached.
the weldment thickness, depression puddle depth exceeds about 60% of
varies linearly with arc pressure. For the weldment thickness. Puddle width
Conclusions
greater amounts of puddle distortion, at the heated surface is relatively
energy from the arc is applied at a level insensitive to changes in surface The employment of an analytical
sufficiently below that of the undis tension. For the case of N = 0.1 N/m model to simulate weld puddle distor
torted weldment such that the result (0.0006 lb/in.), the restraint forces tion and sink due to electromagneti
ing depth of puddle penetration is introduced by the surface tension are cally induced arc pressure acting on
significantly greater than the penetra so small that the puddle distorts so the weld puddle and gravitational
tion that would have occurred had the severely that an ill-behaved finite forces in the puddle has produced the
puddle surface not been depressed. element solution results. following results and conclusions:
Since enhanced penetration is accom Similar effects of low surface ten 1. Distortion of the weld puddle
panied by increased weld puddle sion are shown in Fig. 7. For a very contributes significantly to the pene
width (see Fig. 2) and, therefore, small exposure time of 1.6 s, the tration characteristics of the weld. For
volume, and since it is only molten magnitude of puddle depression is example, it is demonstrated that the
weld metal that is subject to distortion extremely high when N = 0.1 N/m propensity of a weld bead to fully
by arc pressure, the greater puddle (0.0006 lb/in.). For the range penetrate the thickness of the weld-
WELDING RESEARCH SUPPLEMENT I 165-s
ment is enhanced by weld puddle pp. 1145-1174. 7. Friedrich, C M., "BESTRAN-A Tech
depression. 4. Friedman, E., "Thermo-Mechanical nique for Performing Structural Analyses,"
2. Arc current influences weld pen Analysis of the Welding Process Using the WAPD-TM-1140, Bettis Atomic Power fab-
Finite Element Method," Trans. ASME, I. oratory, February 1975.
etration from two standpoints: (a)
Pressure Vessel Techn.. Vol. 97, August 8. Timoshenko, S., and Woinowsky-
increased current results in more heat
1975, pp. 206-213. Krieger, S., Theory ol Plates and Shells, 2nd
input from the arc to the workpiece, 5. Friedman, E., and Glickstein, S. S., "An Edition, McGraw Hill, New York, 1959, Ch.
causing more material to be melted; Investigation of the Thermal Response of 13.
and (b) arc pressure increases with the Stationary Gas Tungsten-Arc Welds," Weld 9. Stepanov, V. V., and Nechaev, V. I.,
square of the arc current, producing a ing lournal 55 (12), Dec. 1976, Research "On the Pressure of the Plasma Arc," We/d
greater degree of puddle depression. Suppl., pp. 408-s to 420-s. ing Production, 1974, No. 11, pp. 4-5.
Application of heat at surfaces be 6. Schoeck, P. A., "An Investigation of 10. Glickstein, S. S., and Yeniscavich, W.,
neath the undistorted surface of the the Anode Energy Balance of High Intensity "A Review of Minor Element Effects on the
Arcs in Argon," Modern Developments in Welding Arc and Weld Penetration," Weld
weld further enhances penetration.
Heat Transfer, Academic Press, New York, ing Research Council Bulletin No. 226, May
Penetration becomes sensitive to small 1963, pp. 353-400. 1977.
changes in current when the depth of
the puddle exceeds 60% of the weld I I
ment thickness. —
KNOWN SOLUTION - KNOWN SOLUTION
3. For partial penetration welds,
depression of the top surface of the ••-•-.
-
weld puddle varies linearly with arc
pressure. When full penetration is
•
achieved, weld bead shape changes
are significantly more sensitive to K = 2 GPa \ a = 2 X IO"9
changes in pressure.
4. Both puddle depression and weld
penetration are strongly dependent on
(1
surface tension at the puddle surfaces.
o
The understanding and controlling of -io
surface tension is essential to control LOG K (GPa)
ling weld puddle shape change, as Fig. 8—Effect of puddle parameters a and K on maximum deflection. Surface
well as enhancing penetration. tension = 1 N/m (0.0057 lb/in.)
5. Efforts are required to measure
and control pressure in the welding arc Appendix: Test Problem to where q„ = pressure = 524 Pa (0.076
and to investigate surface tension in Confirm Distortion Model psi); b = bottom surface puddle, or
molten metals. For example, a deter membrane, radius = 3.175 mm (0.125
mination of how minor elements in.); N = surface tension = I N/m
affect surface tension'" would be a A test problem that includes the (0.0057 lb/in.).
major step in controlling both puddle effects of both surface tension and This expression is derived by letting
distortion and weld penetration. In forces transmitted through molten q = q„ = constant in equation (3),
addition, analytical and experimental material was run and compared with evaluating the integrals, and letting
work on fluid motion in the puddle its known solution to ascertain the r = 0.
need to be pursued. reliability of the analytical model. The resulting deflection w(0) = 1.32
Consider the weldment configura mm (0.052 in.), is compared with finite
tion of Fig. 1. Let the molten region be element solutions for various values of
Acfcnow/edgmenl subject only to gravitational forces. For the parameter a, and the bulk modulus
The numerous consultations with a weldment 6.35 mm (0.25 in.) thick, K. The finite element results are given
Dr. S. S. Glickstein are gratefully this is equivalent to a uniform pressure in Fig. 8, which shows maximum
acknowledged by the author. q,„ acting on the bottom surface of the deflection plotted against a for fixed K,
puddle. q„ is given by: and against K for fixed a. The values
finally selected -a = 2 x 10 ", K =
q„ = P g h
References where p = density = 8415 kg/m'1 2 GPa (290 ksi)—yield a maximum
underbead deflection of 1.102 mm
1. Paley, Z„ and Hibbert, P. D., "Compu (0.304 lb/in.'); g = unit gravitational
(0.043 in.) which is 16% less than the
tation of Temperatures in Actual Weld force = 9.80665 N/kg (1 Ibf/lbm);
known deflection. The bulk of this
Designs," We/ding journal, 54 (11), Nov. h = height of molten region = 6.35
error is attributed to the coarse finite
1975, Research Suppl., pp. 385-s to 392-s. mm (0.25 in.).
element mesh employed within the
2. Clickstein, S. S., Friedman, E., and Therefore, q„ = 524 Pa (0.076 psi) is
Yeniscavich, W., "Investigation of Alloy 600 the pressure applied to the circular puddle region (see Fig. 1). Consistent
Welding Parameters," Welding lournal, 54 with the objectives of this investiga
membrane, which simulates the con
(4), April 1975, Research Suppl., pp. 113-s to tion and the uncertainties of the vari
straint effects of the surface tension, at
122-s. ous input parameters (arc pressure,
the bottom surface of the weld
3. Hibbitt, H. D., and Marcal, P. V., "A surface tension, compressibility), a
puddle.
Numerical Thermo-Mechanical Model for 16% discrepancy for the puddle distor
the Welding and Subsequent Cooling of a The maximum deflection w(0), at tions does not alter any of the results
Fabricated Structure," Computers and the weld centerline is given by:
and conclusions.
Structures, Vol. 3, No. 5, September 1973, w(0) = q„ b/(4N)
166-s | IUNE 1978