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APPLICATION OF TfCREE DIMENSIONAL, FINITE ELEMENT ANALYSIS TO ELECTRON BEAM WELDING OF A HIGH PRESSURE COMPRESSOR DRUM ROTOR

John H. Cowles, Jr., Ingenium Technologies Group, Inc.

P.O. Box 566 Somers, CT, USA, 0607 1-0566

Phone: (203)749-4886 / Fax: (203)749-4886 email: itgcowles@ delphi.com

Mark Blanford Engineering and Manufacturing Mechanics

Sandia National Laboratories Albuquerque, NM, USA, 87 185

Phone: (505)844-3127 / Fax: (505)844-9297 email: mlblanf @ sandia.gov

Anthony F. Giamei , United Technologies Research Center

Silver Lane, M.S. 129-22 East Hartford, CT, USA, 06108

Phone: (203)727-7 172 / Fax: (203)727-7879 email: apg@utrc.utc.com

Michael J. Bruskotter United Technologies Pratt & Whitney

400 Main St., M.S. 165-43 East Hartford, CT, USA, 06108

Phone: (203)565-6682 / Fax: (203)565-8249 email: bruskomj @ pwfire.pweh.utc.com

Finite Element Analysis capability for application to welding has been developed and enhanced during a two year Cooperative Research and Development Agreement(CRADA) between Pratt & Whitney, United Technologies Research Center, and Sandia National Laboratories. Because of the nature of electron beam welding at Pratt & Whitney-- set-up is time consuming, the parts to be welded are complicated, and experimentation is costly-- finite element analysis has found many potential applications. The results of most interest in these analyses are the residual stress and final distortion of the component. The work has made use of the Sandia finite element codes JACQ3D, for thermal analysis, and JAS3D, for mechanical analysis. Both codes use an efficient, non-linear conjugate gradient solution technique which enables large problems to be solved on engineering workstations. This presentation describes several technical challenges that were overcome in the application of the Sandia codes to this class of problems. Stress and distortion results predicted for an electron beam weld of a PW4OOO gas turbine engine drum rotor will also be discussed.

DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

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Introduction

An ongoing Cooperative Research and Development Agreement(CRADA) funded in part by Pratt & Whitney and the United States Department of Energy has lead to an enhanced ability to model three dimensional welding phenomena. The CRADA has brought together scientists and welding engineers from Pratt & Whitney, United Technologies Research Center(UTRC), Sandia National Laboratories(SNL), and Ingenium Technologies Group(1TG). The code development work has focused on two finite element codes from SNL: JACQ3D, a finite element code for thermal analysis, and JAS3D, a code for quasistatic structural analysis. These codes utilize an element by element conjugate gradient solver coupled with single integration point elements. The codes are fast and make efficient use of available machine memory. Many potential applications in Gas Tungsten Arc(GTA) and Electron Beam(EB) welding have been identified. The applications in EB Welding are of great interest at this point because the analyses can be accomplished in reasonable time scales relative to the actual weld schedule development time.

The work presented here is a model of the EB welding of a typical PW4000 High Pressure Compressor Drum Rotor. The purpose of the analysis is to predict the residual stresses in the full penetration, or steady-state, region and in the “downslope” region, which is the region where the electron beam power density is gradually reduced following weld closure. The predicted stress results are then compared with experiment. The comparisons are very encouraging and it is expected that the analysis method described here can be used in the overall optimization of the welding parameters for this process.

Modeling Considerations

A major advantage of EB welding is that parts can be welded with less distortion and higher travel speeds than in other methods such as GTA or Plasma Arc welding. For modelers, a small fusion zone with high travel speed translates into stresses that are more localized and temperature gradients that are much steeper. Therefore, less of a structure has to be modeled to calculate accurate stresses, but that portion of the structure that is modeled must have a high density of finite elements.

Geometry

A 20” segment of a typical drum rotor is shown in Figure 1. The model outline shown here has . 6256 elements and 9793 nodes. The weld is a circumferential butt weld, and the weld line can be seen on the right, axial side of the drum rotor. The model as shown has four elements through the thickness on the weld line. This degree of refinement is adequate for thermal analysis of the full penetration EB weld, but not acceptable for partial penetration welds -- as in the downslope region -- or for stress analysis in either the full or partial penetration regions. Since the stresses in EB welding are very localized, a small section of the drum rotor is meshed for the stress calculations. This section is shown in Figure 2. Its dimensions are 50.8 mm(i x), 12.7mm(in y), and 8.89 mm(in z); this model has 16100 elements and 18360 nodes.

Material Properties

The drum rotor material is Inconel 718. Young’s modulus, Poisson’s ratio, yield strength, thermal expansion coefficient, and thermal conductivity versus temperature are all derived from the Aerospace Structural Metals Handbook[ 11. Specific heat values versus temperature are derived from Brooks, et. al.[2]. Because material properties are not well known at high

Figure 1: 20 Degree Segment of HPC Drum Rotor

Figure 2: Mesh Used in Analysis Modeling Region Near the Fusion Zone

temperatures, selecting the proper values is somewhat of an art form. In the case presented here, the modulus@) is ramped down to 0.001Eo at the liquidus temperature and assumed to remain constant above that temperature. To keep the bulk modulus of the material large, Poisson's ratio is made to approach the incompressible limit of 0.5 as the temperature approaches the liquidus and is also kept constant at higher temperatures. The thermal expansion coefficient is entered into JAS3D via thermal strain. The coefficient is kept constant above the maximum temperature found in [ 11 until the liquidus point; from that point upward in temperature, the thermal strain, for stability reasons, is kept constant. The material model used in the analyses is thermo-elastic-perfectly-plastic(i.e. no workhardening). The yield strength follows along the yield curve until the maximum temperature of available data. At that point the yield strength is linearly ramped down to essentially zero, 1. x lo-' of the room temperature value, at the liquidus temperature. The yield strength above this temperature is kept constant.

The conductivity and specific heat are kept constant between their maximum defied temperatures as in [ 1,2] and the melting point. The specific heat is spiked within the liquidus- solidus transition to account for the latent heat effect which for IN 718 is approximated as 314000 J k g over a temperature range of 1204 to 1316 "C. The conductivity is also modified above the liquidus temperature. Through the melting range, its value is ramped up by a factor of three to better model the convective transfer in the weld pool.

Boundary Conditions

All discussion of boundary conditions refers to the mesh shown in Figure 2.

Thermal. The symmetry plane(y = 0, closest to reader) is insulated. The plane at y = 12.7 mm is subjected to an average convective film coefficient as determined from a thermal analysis performed on the rotor geometry shown in Figure 1. This average film coefficient allowed an approximation for the conduction of heat into the rotor's massive rim, web, and bore. The planes at x = 0 and 50.8 mm are insulated. Since the welding process is performed in a vacuum,

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* the top and bottom surfaces(z = 0.0 and 8.89 mm) are assumed to radiate to surr&d%/ which are considered to be at room temperature. The emissivity is taken to be 0.3. Vaporization is taken as a heat loss from elements reaching a temperature greater than the liquidus. The method for calculating heat loss is a modified Langmuir equation as in Bertram, et. al.131. The energy input from the beam in the steady state is applied as a volume flux and is taken as 15000 Watts at an efficiency of 0.75. The efficiency is adjusted so that the melt zone predicted in the analysis has the same width as the actual fusion zone as measured from weld micrographs. In the steady state, the beam is assumed to be cylindrical with a diameter of 1.52 mm. In the downslope region, the heat source is assumed to be ellipsoidal in shape, and the width and depth are determined from experimental measurements. The heat source for the full penetration weld pass starts at the left side of the mesh and progresses beyond the right side. The second weld pass is a partial penetration weld and starts on the left side of the mesh after an appropriate time period. This time period represents the time it would take for the electron beam to traverse the entire drum rotor circumference. The aspect ratio of the beam for the second pass is provided from experiment as the penetration depth decreases to zero through the downslope region.

Mechanical. The nodes on the symmetry plane are fixed in the y direction; the nodes on the y = 12.7 mm plane are considered free as fixing them would be too constraining. The x = 0.0 and 50.8 mm planes are fixed in the x direction. The top and bottom surfaces(z surfaces) are free. The temperatures at each nodal point and increment are input from the results of the thermal analysis.

Finite Element Codes

JACQ3D Program Description. JACQ3D is a finite element computer program for solving the materially-nonlinear heat conduction problem in three dimensions. It will solve both transient and steady-state problems. JACQ3D takes advantage of a nonlinear conjugate gradient iterative technique to solve the finite element equations in the spatial domain. The temporal integration for transient problems uses a second-order Adams-Bashforth predictor with a corrector based on the trapezoid rule. A singular feature of JACQ3D is the use of a one-point integration scheme in an eight-node uniform-flux brick element, which makes the code very fast compared to many commercially-available finite-element heat conduction codes. The zero-energy modes of this element are controlled by hourglass stiffness terms. Bodies under analysis may be loaded by specified surface temperatures, heat fluxes, or volumetric heat generation. Boundary conditions may be specified using convection coefficients or radiation to space. Phase changes are easily simulated using an enthalpy formulation for the variation in heat capacity with temperature.

JAS3D Program Description. JAS3D is a three-dimensional finite element program designed to solve quasistatic nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. Nonlinear iterative methods are used to solve the equations. A wide variety of material constitutive models are available, and sliding interface logic is implemented. Two Lagrangian uniform-strain elements are available: an eight- node hexahedron for solids and a four-node quadrilateral for shells. Both use hourglass stiffness to control zero-energy modes. Bodies under analysis may be loaded by surface pressures and concentrated forces, specified displacements, or body forces from gravity or thermal expansion. Neither JACQ3D nor JAS3D require the formation of the entire stiffness matrix for a given problem, therefore the codes are far less memory intensive than commercially available general- purpose codes, enabling them to solve large problems efficiently on engineering workstations.

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Significant Problems Overcome

In solving the mechanical analysis, two major obstacles were overcome so that the predicted stresses varied smoothly in space. The analysis presented does not use the concept of a "cutoff" temperature, so the behavior of the material model and the finite element assumptions must not lead to inaccuracies at temperatures above the liquidus point. The first problem to be overcome was the calculated stress within the weld pool. The stresses were hydrostatic in nature and varied between +/- 10 MPa even though the yield strength is much lower than this. It was felt that this phenomena occurred for two reasons: 1) the mesh is too coarse within the weld pool to allow the free surfaces to properly zero the stresses, and 2) the finite element model cannot properly account for the full free surface when an EB weld is in keyhole mode. By forcing the hydrostatic stresses in the weld pool to zero, the problem was eliminated.

Another problem encountered after some of the initial EB weld analyses was that the residual stresses in the fusion zone region were largely oscillatory in nature yielding results that varied +/- 500 MPa from an average. This was traced to the numerical procedure used in JAS3D to resist the hourglassing modes of the single-point integrated linear hexahedral elements. The excitation of hourglass(or zero-energy) modes can lead to severe, unresisted mesh distortion. JAS3D uses an algorithm developed by Flanagan and Belytschko [4] to isolate and control the hourglass modes independently of the rigid body and uniform strain modes of the element. The algorithm develops a resisting force based on the cumulative deformation of the element. Each increment of the accumulated force is scaled to be small compared to the current effective modulus of the material. In a welding simulation, material in the weld pool begins very stiff, undergoes melt, and then resolidifies. When the material has melted, the incremental contribution to the hourglass resistance in a given load step is suitably small. However, the accumulated forces include contributions from early load steps which are based on the initial elastic stiffness of the material. Thus the hourglass resisting forces can easily dominate the solution in the weld pool, leading to nonphysical distortions and stresses.

This problem was addressed by turning off dl accumulation of hourglass forces before and during melt, so that the code only uses the current incremental response in calculating the hourglass resistance. This is sometimes known as hourglass "viscosity" as opposed to hourglass "stiffness", and is often used in transient-dynamic calculations.

Computational Hardware and Analysis Times:

The computations were performed on an IBM 370 RS 6000 workstation with 128 MBytes of RAM and 1 GByte free disk storage space. The thermal analysis included 1930 increments and took approximately 1.5 CPU hours. The mechanical analysis included 14.41 increments and took approximately 206 CPU hours.

Results

Discussion

The thermal profile for the fidl penetration, initial pass weld is shown in Figure 3. The maximum temperature of 1210 "C is the approximate liquidus temperature for the material. The "A" contour is an approximation of the weld pool boundary in the quasi-steady-state weld case. The x(hoop), axial), and z(through thickness) components of stress are contoured in Figures 4, 5, and 6 respectively. The maximum temperature of the mesh at this point is slightly below 200 O C . Since the yield strength of the material between this temperature and ambient varies only slightly, the stresses calculated at this point are treated as if they were residual stresses for discussion purposes. The maximum stresses are at the center of the material thickness in all

1210.= A

1040.= B

870.= f

'loo.= D

530.= E

360.= F

190.= 6

2 0 . k H

Figure 3: Temperature Distribution During First Pass, Full Penetration EB Weld

Figure 4: Hoop Stress(&) Upon Cool- Down After Full Penetration EB Weld (Cutting plane at x = 17.8 mm)

946.= a

719.= B

491.= c

4 1 9 s 0

- 6 4 6 . ~ H

Figure 5: Axial Stress(0,) Upon Cool- Down After Full Penetration EB Weld (Cutting plane at x = 17.8 mm)

Figure 6: Through-Thickness Stress(o,) Upon Cool-Down After Full Penetration EB Weld (Cutting plane at x = 17.8 mm)

cases. The stresses in this region are somewhat hydrostatic. In this region, while the von Mises stress is at the yield strength of 1240 MPa, the hoop component of stress is significantly larger. It can be seen that the through thickness component of stress on the top and bottom free surfaces is essentially zero(1ess than 5% of peak stresses) showing that the mesh is adequate for this analysis. The axial component of stress is compressive on the top and bottom surfaces of the fusion zone but is tensile in the center.

The thermal profile within the downslope region is shown in Figure 7. It can be seen that the weld pool is much smaller and is rising upwards in the z direction as the electron beam power density is reduced. The full model is shown with the hoop), y(axial), and z(through thickness) components of residual stress(i.e. temperatures at ambient) contoured in Figures 8,9, and 10 respectively. The x component of stress(ho0p direction) on the left, top(outer diameter) surface is nearly equal to the quasi-steady-state value on the top fusion zone surface shown in Figure 4. It then becomes more tensile toward the end of the downslope region. The hoop stress on the

m 0

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I

1210. = A 1375.= A

1040.= B llOO.= B

870.= C 825.= C

700.= D 550.= D

530.= E 215.= E

360.= F O.= F

-215.~ G

- 5 5 0 . ~ H

190.= c

20.0= H

Figure 7: Temperature Distribution During Downslope, Partial Penetration Weld

Figure 8: Hoop Stress(0,) Upon Cool- Down After All Welding

869.=

581.=

294.=

6.41=

-281.=

-568.~

-856.~

I181 .= A

948.= B

709.= C

470.= D

230.= E

-8.80= P

-248.= G

-1143.= H \ -487 .= H

Figure 9: Axial Stress(0,) Upon Cool- Down After All Welding

Figure 10: Through-Thickness Stress(cr,,) Upon Cool-Down After All Welding

lower sut-face(inner diameter) is not as affected by the relative location in the region. As one progresses through the downslope region from left to right along the top surface the trend of the axial stress is to go from compressive to tensile; the bottom surface axial stress sees the opposite trend. The through thickness stress in the mid-section decreases toward the end of the downslope region where it then transitions back to its steady-state value.

Comparison With Experiment d 0 -b OG

Table I shows the comparison of the experimentally derived hoop and axial stresses with those calculated at the outer diameter, mid-section, and inner diameter where available. The experimental stresses are derived via a strain gage and hole drilling technique. The stresses at the I.D. and O.D. are averages of three measurements; the mid-section stresses are single measurements. Unfortunately, this method is not very accurate in regions of high stress gradient which is the case here. The error in the measurements shown is as high as 350 MPa.

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% Table I: Experimental and Analytical Residual Stresses: Steady State and Downslope Regions

Circumferential Through Thickness Axial Stress(MPa) Hoop Stress(MPa) Location Location ExperimentIAnalysis ExperimendAnalysis

Steady State Region O.D. - 1951-725 64615 10 Mid Section -24 1/4 13 607/137 8 I.D. -2481-725 56 115 10

80% Downslope Reg. O.D. 341-565 60918 82

The pattern of the calculated stresses and the experimental data compare reasonably well, with the exception of the mid-section values, given the possible error in the data discussed above and the geometric and material behavior assumptions made in the analysis. The calculated stresses are in general too high, while the stresses in the mid-section of the fusion zone after the full penetration weld are calculated to be tensile with a hydrostatic component; this hydrostatic component is not present in any of the experimental data. Assumptions that could cause the overprediction of stresses might be the lack of rate dependence in the material model at elevated temperatures, the fact the small section analyzed is in effect over-constrained in the x direction, or related to the arbitrary zeroing of the weld pool hydrostatic stresses.

Conclusions and Future Work

The pattern, but not yet the magnitude, of the calculated residual stresses is reasonable, with the exception of the mid-section values, after each of the quasi-steady and downslope weld passes. The magnitudes of the stresses are in general too high and at the mid-section the residual stresses are predicted to have a tensile hydrostatic component that does not agree with experiment. The source of these hydrostatic stresses is unknown at this time; however, it is expected that they could be caused by one of the following: temperature changes over stress increments being too large, the mesh in the fusion zone being too coarse, or a material model that lacks some fundamental volumetric inelastic deformation mechanism during the cool down after welding.

It would be desirable to increase the mesh density within the fusion zone for the 20° segment mesh shown in Figure 1 and run the current set of analyses using this geometry. The source of the hydrostatic tensile stresses in the fusion zone mid-section needs to be tracked down and an appropriate measure taken to avoid it. The results of this new analysis can then be used to aid in the optimization of the welding parameters with the aim of reducing the overall magnitude of the stresses within and near the fusion zone. Parameters to be varied might include: the beam diameter, the travel speed, the input power, and the length of the downslope region.

References

1. W.F. Brown, Jr., H. Mindlin, CY. Ho, eds., Aerospace Structural Metals Handbook, (CINDASKJSAF CRDA Handbooks Operation, Purdue Univ., W. Lafayette, IN, Vol. 4,1994)

2. C.R. Brooks, M. Cash, A. Garcia, ‘“The Heat Capacity of Inconel 718 From 3 13 to 1053 K,” Journal of Nuclear Materials, 78( 1978), 419-421.

3. L.A. Bertram, R.S. Larson, S.K. Griffiths, “Diffusion Limits to Metal Evaporation from Weld Pool Surfaces,”(Sandia National Laboratories, Internal Memorandum, Sept. 22,1989)

4. D.P. Flanagan, T. Belytschko, “A Uniform Strain Hexahedron and Quadrilateral With Orthogonal Hourglass Control,” Int. J. for Num. Meth. in Em., 17(1981), 679-706.