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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

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