INVESTIGATIVE STUDY OF 2-D VS. 3-D WELD RESIDUAL STRESS ANALYSES OF THE NRC PHASE II MOCKUP

Transcription

1 Proceedings of the ASME 212 Pressure Vessels & Piping Conference PVP212 July 15-19, 212, Toronto, Ontario, CANADA PVP INVESTIGATIVE STUDY OF 2-D VS. 3-D WELD RESIDUAL STRESS ANALYSES OF THE NRC PHASE II MOCKUP Francis H. Ku Structural Integrity Associates, Inc Hellyer Avenue, Suite 21 San Jose, California 95138, USA Shu (Stan) S. Tang Structural Integrity Associates, Inc Hellyer Avenue, Suite 21 San Jose, California 95138, USA ABSTRACT Finite element weld residual stress analyses are performed to investigate the similarities and differences between twodimensional (2-D) and three-dimensional (3-D) finite element analyses on weld residual stress predictions of the NRC Phase II Mockup. The Mockup resembles a typical pressurized water reactor (PWR) surge nozzle of 14 in diameter which includes a dissimilar metal weld (DMW) connecting the safe end and a stainless steel weld (SSW) connecting the surge line piping. The 2-D analysis employs axisymmetric modeling approach, while the 3-D analysis utilizes moving heat source approximation techniques. The results demonstrate the variations in residual stresses among the weld bead start and stop locations. Comparing the 2-D and 3-D residual results against experiment measurements also reveal the limitations inherent to the 2-D analysis, while the 3-D analysis can produce results that are of closer match to experimental measurements. BACKGROUND A mockup of a surge nozzle, without a weld overlay (WOL), is fabricated under the U.S. Nuclear Regulatory Commission (NRC) Phase II International Round Robin Weld Residual Stress Finite Element Analysis Model Validation Program [1, pp ]. The purpose of this effort is to conduct a blind validation of finite element analysis (FEA) predictions to experimental measurements. In this paper, the FEA results are compared to published incremental hold drilling (idhd) and deep hold drilling (DHD) measurements. The mockup includes a dissimilar metal weld (DMW) between the nozzle and the safe end, followed by an inside diameter (ID) back weld at the root of the DMW, and a stainless steel weld (SSW) connecting the safe end to the piping [2, p. 187], as shown in Figure 1. Through-wall idhd and DHD measurements along the centerline of the dissimilar metal weld (DMW) are performed [2, p. 187], as shown in Figure 2. The analyses presented in this study consist of FEA results using two-dimensional (2-D) axisymmetric and threedimensional (3-D) solid models of the Phase II mockup. The analyses include weld residual stress (WRS) predictions from DMW and machining, ID back welding and machining, and SSW machining and welding. Post-weld heat treatment, creep, phase transformation, and annealing were not considered. FIG. 1 PHASE II MOCKUP GEOMETRY 1 Copyright 212 by ASME

2 FIG. 2 EXPERIMENTAL MEASUREMENT LOCATIONS ANALYTICAL MODEL Weld induced residual stress analyses are nonlinear, pathdependent problems as a result of the cumulative stress-strain cycling history inherent with the heating and cooling of materials during the welding process. The 2-D and 3-D WRS FEA are performed using the ANSYS finite element software package [3]. Each WRS FEA is performed as a continuous analysis so that the temperatures and stress histories from different welds are taken into account the residual stresses and strains caused by the previous weld pass are used as initial conditions for the next weld pass. Analytically, the deposition of the weld metal is simulated by imposing a triangular heat generation function on the elements representing the active weld nugget for each weld, as illustrated in Figure 3. In ANSYS, the heat generation applied to the weld nuggets is a volumetric energy rate, as energy per volume per time. For the 2-D analysis, the heat generation rate to be input in ANSYS is the heat efficiency ( ) times the calculated total heat input (Q L ) divided by the weld bead area and the ramp time (t ramp ): HGEN Q A t bead L ramp In the thermal pass, a real-time temperature control algorithm is implemented into the heat generation application such that heat is turned off when the average temperature within the active weld nugget has reached the melting temperature. Note that the algorithm evaluates the active weld nugget as a whole, so there are nodes within the nugget that can reach beyond the melting temperature as heat will be continuously added to it until the average temperature of the entire nugget reaches the melting point. In the stress pass, a plateau temperature at the melting point is applied during the temperature import because temperature beyond melting point is not meaningful in the residual stress calculation. This additional temperature control algorithm restricts the maximum achievable temperature to melting point where the strength of the molten metal is negligible. A pictorial illustration of the heat input application is shown in Figure 3. For the 3-D weld residual stress simulation, each weld bead is divided into multiple discrete weld nuggets to approximate weld head traveling during welding. The moving heat source from the weld head traveling is approximated using the continuous nugget progression (CNP) technique developed for 3-D weld residual stress analyses [4]. The CNP technique is specially developed and encoded in forms of ANSYS macros where the weld nugget segments within each weld bead ring are deposited continuously in sequence without intermediate cooling until the last nugget within the bead ring. For small weld nuggets where each is the size of a discrete weld bead formed via a momentary weld action, this approach approximates the continuous welding progression in the physical situation without much sacrifice in computation time, where the logic progresses to the next contiguous nugget as soon as the active nugget has been deposited "hot" and continues to cool down. Energy Q Real time checking of nugget temperature For the 3-D analysis, the heat generation rate to be input in ANSYS is the heat efficiency ( ) times the above unit length heat input (Q L ) divided by the weld bead volume (V bead ) and the ramp time (t ramp ): Q HGEN V t L bead ramp Weld bead t ramp Time The total heat input is imposed onto the active nugget simultaneously, which is conservative and often results in extremely high temperatures (above melting point) during the heat generation period. Temperatures beyond melting point already represent molten material; any additional heat essentially produces no additional thermal benefit and, therefore, the heat input can be turned off at this point. The temperature predictions using this approach are consistent with the thermal couple measurements for this mockup. FIG. 3 HEAT INPUT APPLICATION SCHEMATICS WELD RESIDUAL STRESS ANALYSIS The WRS analysis utilizes a decoupled multi-physics simulation process, which consists of a thermal pass to 2 Copyright 212 by ASME

3 determine the temperature distribution history due to the welding process, and a stress pass to calculate the residual stresses throughout the thermal transient history. It is reasonable and generally acceptable to assume that the geometric distortions induced by the welding process are not significant when comparing to the overall geometry; i.e. the overall geometry remains fairly the same throughout the welding process. Therefore, the thermal and stress phases of the welding simulation can be decoupled as two separate FEA simulations. The element birth and death feature in ANSYS allows for the deactivation (death) and reactivation (birth) of the elements stiffness contribution when necessary. This feature is used such that weld bead elements that have not yet been deposited are deactivated (via EKILL command) because they have no contribution to that particular step of the FEA. The deactivated elements have near-zero conductivity and stiffness contribution to the structure. When the weld bead elements are required in a later step, they are then reactivated (via EALIVE command). The element birth and death feature can also be utilized to activate and deactivate appropriate components during specific steps of the analysis. When combined with appropriate material changes, the model can be used to represent the changing material and component configurations at any particular step of the analysis. MATERIAL PROPERTIES Simulation of weld residual stresses requires adequate characterization of material properties in the plastic range. These material properties are specially developed by Structural Integrity Associates, Inc. (SIA) for weld residual stress analyses that have demonstrated to produce residual stress predictions in good agreement with experimental measurements, such as those used in the NRC Phase IV weld overlay mockup study [1, pp ]. In the analysis, multi-linear isotropic hardening material behavior is assumed for all the materials. The use of the isotropic hardening model assumes that the yield surface will expand with increasing plastic strain but will retain the same initial shape. It should be noted that the temperature dependent stress-strain curves for the materials are capped off at the material flow stress at temperatures to minimize the overprediction of residual stresses from using the isotropic hardening law: It should be noted that the stress-strain curves shown in Figure 1 are capped off at the material flow stress ( f ), which is defined as the average of the yield strength ( y ) and ultimate tensile strength ( u ), at temperatures to minimize the overprediction of residual stresses from using the isotropic hardening law: y u f 2 The modified temperature dependent stress-strain curves for the Alloy 82/182 DMW material is shown in Figure 4. True Stress (ksi) FIG. 4 MODIFIED SS CURVES FOR ALLOY 82/182 FINITE ELEMENT MODELS True Strain (in/in, mm/mm) 7 F (21 C) 5 F (26 C) 7 F (371 C) 11 F (593 C) 15 F (816 C) 25 F (1371 C) Two finite element models are developed for this study: a 2- D axisymmetric model and a 3-D solid model. The developed 2-D axisymmetric finite element model is shown in Figure 5, and Figure 6 for the 3-D model. The 3-D model is a quarter model representing a 9 section of the mockup geometry. The weld beads are modeled one by one as weld nuggets. The weld bead layout approximates the shapes measured by a laser profilometer [2, p. 188], as shown in the comparisons between the laser profilometer measurements (Figures 7 and 8) and the finite element models (Figures 9 and 1). Figure 9 shows the cross-section view of the weld nugget pattern in the finite element models, while Figure 1 shows the weld nugget segments in the 3-D model. Note that each 3-D nugget segment is of 3 arc, and the welding direction is chosen to be stacked; this enables the 3-D analysis to provide three types of results for comparison: bead start, mid-span, and bead stop, as shown in Figure 6. FIG. 5 2-D FINITE ELEMENT MODEL True 3 Copyright 212 by ASME

4 Start Welding Direction Mid-span Stop FIG. 6 3-D FINITE ELEMENT MODEL FIG. 9 CROSS SECTION WELD NUGGET PATTERN FIG. 7 DMW LASER PROFILOMETRY FIG. 1 3-D WELD NUGGET SEGMENTS (3 ARC) RESULTS COMPARISONS AND DISCUSSIONS It was noted during the referenced NRC Public Meeting that, the axial and hoop measurements for post-safe end weld were inadvertently switched [2, pp ]. The issue has been corrected for the results comparisons presented and discussed herein. All comparison plots show vs. Radial distance from DMW ID surface (mm). FIG. 8 ID BACK WELD LASER PROFILOMETRY 2-D Predictions vs. idhd Measurements As shown in Figures 11 through 14, the first set of comparisons highlights the FEA predictions using the 2-D axisymmetric model. In general, the 2-D FEA predictions compare fairly well with the idhd measurements. Another important observation is that, all 2-D results overpredict the tensile weld residual stresses on the ID surface (at mm). The 2-D predictions are conservative when looking from the ID crack initiation perspective. 4 Copyright 212 by ASME

5 Pre Safe End Weld Axial Residual Stress Post Safe End Weld Hoop Residual Stress D FEA Bead Start 2 1 3D FEA Bead Start D FEA Bead Stop 9 3 3D FEA Bead Stop FIG D COMPARISON FOR PRE-SSW AXIAL WRS FIG D COMPARISON FOR POST-SSW HOOP WRS Pre Safe End Weld Hoop Residual Stress D FEA Bead Start 3D FEA Bead Stop 9 3-D Predictions vs. idhd Measurements As shown in Figures 15 through 18, the second set of comparisons highlights the FEA predictions using the 3-D solid model. It case be seen that, when compared to the 2-D results, the 3-D FEA predictions offer improvements in reducing the residual stress over-prediction on the ID surface. The most significant improvement is on the Post-SSW hoop residual stress (Figure 18), where the 3-D results track the measurements better than the 2-D results. Moreover, the 3-D mid-span results yield the best comparison to the measurements among the three azimuths. This is expected because the mid-span azimuth is remote from the bead start/stop locations, which is a closer representation of the actual DMW state of the mockup. FIG D COMPARISON FOR PRE-SSW HOOP WRS Pre Safe End Weld Axial Residual Stress Post Safe End Weld Axial Residual Stress D FEA Bead Start 3D FEA Bead Stop D FEA Bead Start 3D FEA Bead Stop 9 FIG D COMPARISON FOR PRE-SSW AXIAL WRS FIG D COMPARISON FOR POST-SSW AXIAL WRS 5 Copyright 212 by ASME

6 6 5 Pre Safe End Weld Hoop Residual Stress This observation is not surprising as each weld nugget in the 2-D axisymmetric model represents a 36 weld ring, so any azimuth around the circumference is a bead start point. 4 3 Pre Safe End Weld Axial Residual Stress D FEA Bead Start 3D FEA Bead Stop D FEA Bead Start FIG D COMPARISON FOR PRE-SSW HOOP WRS Post Safe End Weld Axial Residual Stress D FEA Bead Stop FIG D VS. 3-D FOR PRE-SSW AXIAL WRS 4 3 Pre Safe End Weld Hoop Residual Stress D FEA Bead Start 3D FEA Bead Stop D FEA Bead Start FIG D COMPARISON FOR POST-SSW AXIAL WRS Post Safe End Weld Hoop Residual Stress D FEA Bead Stop FIG. 2 2-D VS. FOR PRE-SSW HOOP WRS 4 3 Post Safe End Weld Axial Residual Stress D FEA Bead Start 3D FEA Bead Stop D FEA Bead Start FIG D COMPARISON FOR POST-SSW HOOP WRS 2-D vs. 3-D Predictions D FEA Bead Stop 9 As shown in Figures 19 through 22, the last set of comparisons highlights the FEA predictions between the 2-D axisymmetric and the 3-D solid models. It case be seen that, the 2-D results appear to compare better with the 3-D Start results. FIG D VS. FOR POST-SSW AXIAL WRS 6 Copyright 212 by ASME

7 Post Safe End Weld Hoop Residual Stress FIG D VS. FOR POST-SSW HOOP WRS 3D FEA Bead Start 3D FEA Bead Stop 9 REFERENCES 1. U.S. NRC Category 2 Public Meeting Summary, ML , Phase II Internal WRS Round Robin Data Analysis. Rockville, MD, June 14 15, U.S. NRC Category 2 Public Meeting Summary, ML124541, PWR Materials Reliability and Weld Repair Research, Charlotte, NC, January 24 26, ANSYS Mechanical APDL and PrepPost, Release 13. (w/ Service Pack 2) x64, ANSYS, Inc., Canonsburg, PA, March F.H. Ku, P.C. Riccardella, Fast Three-Dimensional Finite Element Analysis of Weld Overlay Application on a Formed Feeder Elbow, PVP , Proceedings of the ASME 211 Pressure Vessel & Piping Division Conference, ASME, New York, NY, 211. CONCLUSIONS Two-dimensional and three-dimensional finite element analyses have been performed to evaluate the weld residual stresses within the dissimilar metal weld of a 14 surge nozzle mockup. FEA predictions have been compared to idhd experimental measurements through the centerline of the DMW, and results have demonstrated that: 1) Both 2-D and 3-D predictions agree well with idhd measurements. 2) Conservative predictions on ID surface when using 2-D model. 3) 2-D results compare closer to the 3-D results for the bead start location. 4) 3-D results yield better agreements with measurements 5) Modified stress-strain curve combined with isotropic hardening is suitable for WRS FEA: a) Easy to obtain or derive stress-strain data b) More stable and faster solution convergence than mixed-mode hardening law c) Improved accuracy of weld residual stress predictions over traditional kinematic and isotropic hardening laws using unmodified strain-strain curves d) Does not over-predict weld residual stresses Overall, the 3-D analyses produce the best results. With ever increasing computational power, 3-D models are recommended for more accurate prediction of weld residual stresses. In addition, moving heat source type of 3-D analyses can be done fairly easily through the use of streamlined scripts and automation routines in the FEA code. 7 Copyright 212 by ASME