Thermo-Structural Coupled Analysis of Skirt-to-Shell Weld Overlay Formed Structures
1. Definition and Fundamental Principles
The thermo-structural coupled analysis of skirt-to-shell weld overlay formed structures represents an advanced computational methodology used to evaluate the interaction between thermal fields and mechanical stress fields during and after weld overlay operations on pressure vessel support structures. In pressure vessel engineering, the skirt serves as the primary vertical load-bearing support connecting the vessel shell to its foundation. When overlay cladding is applied to the skirt-shell joint region to provide corrosion or erosion resistance, the welding thermal cycle induces complex transient temperature distributions that generate residual stresses, microstructural transformations, and geometric distortions.
This coupled analysis integrates two physically interdependent phenomena:
- Thermal field analysis: Models the transient heat conduction, convection, and radiation during the welding process, capturing the rapid heating and cooling cycles that characterize TIG or MIG weld overlay operations on thick skirt and shell geometries.
- Structural field analysis: Solves the mechanical equilibrium equations under the imposed thermal strains, plastic deformation, and phase transformation strains arising from the welding thermal cycle.
The coupling is inherently sequential: the thermal analysis provides temperature history inputs to the structural solver, while structural deformations (particularly gap changes and contact conditions) can feed back into the thermal model in fully coupled formulations. For skirt-to-shell overlay structures, this coupling is particularly critical due to the geometric discontinuity at the joint, the high constraint imposed by the thick skirt geometry, and the multi-pass nature of overlay welding.
2. Technical Purpose and Engineering Value
2.1 Primary Objectives
The thermo-structural coupled analysis of skirt-to-shell weld overlay structures serves several critical engineering objectives:
- Residual stress prediction: Quantify the magnitude, direction, and distribution of residual stresses in the overlay weld metal, heat-affected zone (HAZ), and base metal of both the skirt and shell components.
- Distortion assessment: Predict angular distortion at the skirt-shell joint and global deformation of the vessel support structure that could affect installation tolerances and structural integrity.
- Crack susceptibility evaluation: Identify regions of high tensile residual stress combined with susceptible microstructures that may lead to cold cracking, hydrogen-induced cracking, or stress corrosion cracking.
- Process optimization: Determine optimal welding sequences, interpass temperature controls, and preheating strategies to minimize adverse residual stress states.
- Structural integrity verification: Provide quantitative stress data to support fitness-for-service assessments and remaining life evaluations of overlay-clad skirt structures.
2.2 Contribution to Company Capabilities
This analytical competency directly enhances Cladding Technology Shanxi Co., Ltd.'s qualification building and product delivery capabilities in the following ways:
- Supports WPS (Welding Procedure Specification) qualification by providing predictive stress data that validates welding sequences and parameters.
- Reduces the need for extensive destructive testing through validated computational predictions.
- Enables engineering justification for customers regarding the structural integrity of overlay-clad skirt assemblies.
- Facilitates troubleshooting of field issues such as cracking, excessive distortion, or stress-related failures.
3. Key Analysis Methodology and Implementation Points
3.1 Finite Element Model Configuration
The accuracy of thermo-structural coupled analysis depends critically on the fidelity of the finite element model. Key modeling considerations for skirt-to-shell overlay structures include:
| Model Parameter | Recommended Approach | Rationale |
|---|---|---|
| Element Type | 8-node brick elements with reduced integration (SOLID186/SOLID276 in ANSYS) | Accurately captures 3D stress states at geometric discontinuities |
| Mesh Density | Element size ≤ 1/3 of overlay bead width; refinement within 3× HAZ width | Resolves steep thermal gradients and plastic strain localization |
| Thermal BCs | Convective-radiative boundaries; moving heat source (Gaussian double-ellipsoid) | Realistic representation of TIG/MIG heat input and ambient cooling |
| Mechanical BCs | Fixed support at skirt bottom; symmetry conditions where applicable | Represents actual support conditions during fabrication |
| Material Model | Temperature-dependent elastic-plastic with phase transformation strains | Captures thermal softening, yield surface evolution, and TRIP effects |
| Welding Sequence | Layer-by-layer, pass-by-pass activation with proper cooling intervals | Accurately simulates multi-pass overlay buildup |
3.2 Thermal Analysis Key Parameters
The thermal analysis models the transient temperature field using the following governing equation:
∂/∂x[λ(∂T/∂x)] + ∂/∂y[λ(∂T/∂y)] + ∂/∂z[λ(∂T/∂z)] + Q = ρc(∂T/∂t)
Where the heat source Q is defined as a double-ellipsoidal Gaussian distribution for MIG welding or a single-ellipsoidal distribution for TIG welding. Critical thermal parameters include:
| Parameter | Typical Range (Skirt-Shell Overlay) | Influence on Analysis |
|---|---|---|
| Welding current | 100–250 A (TIG); 200–400 A (MIG) | Determines peak temperature and HAZ width |
| Travel speed | 3–12 cm/min | Affects heat input and thermal gradient steepness |
| Heat input | 0.5–4.0 kJ/mm | Primary driver of residual stress magnitude |
| Preheat temperature | 50–250°C (depending on base material) | Reduces thermal gradient and hydrogen cracking risk |
| Interpass temperature | 50–200°C | Controls cooling rate and microstructural evolution |
| Cooling rate (800→500°C) | 5–80°C/s | Determines HAZ microstructure and hardness |
3.3 Structural Analysis Key Considerations
The structural analysis employs an elastic-plastic constitutive model with the following strain components:
- Elastic strain: Derived from Hooke's law with temperature-dependent Young's modulus and Poisson's ratio.
- Thermal strain: ε_th = α·ΔT, where α is the temperature-dependent coefficient of thermal expansion.
- Plastic strain: Computed using the flow stress curve at the current temperature, accounting for thermal softening.
- Phase transformation strain: Volumetric expansion associated with austenite-to-ferrite/martensite transformations in the HAZ.
- Creep strain: May be relevant for high-temperature service conditions post-overlay.
The governing mechanical equation is:
∇·σ + f = 0, where σ = D:(ε - ε_th - ε_pl - ε_tr)
3.4 Welding Sequence Optimization
For skirt-to-shell overlay structures, the welding sequence has a profound effect on the final residual stress state. The following strategies are validated through coupled analysis:
- Symmetrical welding: Alternating welds on opposite sides of the skirt to cancel angular distortion.
- Back-step welding: Reducing longitudinal residual stress accumulation in the overlay direction.
- Stress-relief passes: Incorporating planned stress-relief welds in low-stress regions.
- Sequential layer build-up: Optimizing the number of layers and passes to distribute thermal input evenly.
4. Applicable Standards and Acceptance Criteria
4.1 Design and Fabrication Standards
| Standard | Relevant Requirements | Application to Analysis |
|---|---|---|
| GB 150.1–150.4 | Pressure vessel design, fabrication, and inspection | Defines allowable stress values and joint efficiency for skirt-shell assemblies |
| NB/T 47013.2 | RT acceptance criteria for welds | Quality level requirements for overlay weld NDT |
| NB/T 47013.3 | UT acceptance criteria | Acceptance criteria for overlay weld thickness and defect detection |
| ASME BPV Section VIII Div. 2 | Alternative rules for pressure vessels | Permits FEA-based qualification of weld overlay procedures |
| ASME BPV Section IX | Welding qualifications | WPS/PQR requirements that the analysis supports |
| ASTM A388 | Weld overlay of carbon and low-alloy steels | Material and procedure requirements for overlay welding |
| ASTM A240 | Stainless steel plate/sheet for cladding | Overlay material specifications |
| API 510 | Pressure vessel inspection code | Residual stress acceptance for in-service equipment |
| ISO 15614-1 | Welding procedure qualification | International qualification framework |
| NACE MR0175 / ISO 15156 | Materials for H₂S environments | Overlay material selection criteria for sour service |
4.2 Residual Stress Acceptance Criteria
The following acceptance criteria are commonly applied to evaluate the results of thermo-structural coupled analysis for skirt-to-shell overlay structures:
- Maximum tensile residual stress: Should not exceed 0.5×σ_y (yield strength of the overlay material at operating temperature) in the overlay weld metal.
- Stress gradient: Maximum stress gradient at the overlay/base metal interface should be controlled to minimize crack initiation risk.
- Distortion limits: Angular distortion at the skirt-shell joint should not exceed 1:100 of the joint length; overall vessel verticality deviation should remain within ±L/1000.
- Post-weld heat treatment (PWHT) effectiveness: Analysis should demonstrate that residual stresses are reduced to ≤50 MPa after PWHT, consistent with ASME BPV Section VIII requirements.
5. Common Risks and Mitigation Controls
5.1 Technical Risks
| Risk | Root Cause | Mitigation Strategy |
|---|---|---|
| Hydrogen-induced cracking | High cooling rate + high diffusible hydrogen + high residual stress | Preheat to ≥150°C; control interpass temperature; use low-hydrogen consumables; validate with coupled analysis |
| Excessive angular distortion | Asymmetric thermal input at skirt-shell joint | Symmetrical welding sequence; backing bar support; real-time monitoring; predictive FEA guidance |
| Overlay spallation/delamination | High tensile residual stress at overlay interface + poor metallurgical bonding | Optimize heat input; validate dilution ratio; apply stress-relief passes; confirm bond strength testing |
| Hot cracking in overlay | Solidification cracking in weld metal due to segregation | Control dilution ratio; select appropriate filler metal; manage cooling rate through preheat |
| Model prediction inaccuracy | Overly simplified boundary conditions or material models | Validate model against strain gauge measurements; use temperature-dependent properties; incorporate phase transformation |
5.2 Quality Control Integration
The results of thermo-structural coupled analysis should be integrated into the company's quality management system as follows:
- Analysis results feed into the WPS development process, providing engineering justification for welding sequences and parameters.
- Predicted high-stress regions are flagged for enhanced NDT (UT/MT) during fabrication.
- Strain gauge validation points are incorporated into the first-article qualification procedure.
- Analysis outputs are documented in the project quality plan and made available for customer review.
- Post-fabrication residual stress measurements (X-ray or neutron diffraction) are compared against predictions to continuously improve model accuracy.
6. Application Across Company Technology Routes
6.1 TIG/MIG Weld Overlay Route
Thermo-structural coupled analysis is most directly applicable to the TIG/MIG weld overlay route, which is the company's primary overlay fabrication method. Key applications include:
- Multi-pass overlay sequence design: Predicting the cumulative residual stress state after each pass to optimize the welding sequence for skirt-to-shell joints. TIG overlay (typically 100–180 A) produces lower heat input but requires more passes for thick overlays, creating complex thermal cycling.
- Hot wire TIG (HWT) optimization: For thick overlay deposits (≥3 mm) on skirt structures, HWT processes combine TIG arc heating with a heated filler wire. Coupled analysis models the dual heat source to predict optimal wire preheat temperature and wire feed rate.
- Submerged arc overlay (SAW): For heavy-duty overlay applications on skirt structures requiring thick cladding (≥5 mm), SAW provides higher deposition rates. The coupled analysis accounts for the flux-covered heat input distribution.
- Distortion control for thin-wall skirt shells: Where skirt shell thickness is limited (e.g., 12–20 mm), coupled analysis is essential to predict and control distortion that could compromise the skirt's load-bearing capacity.
6.2 Hydraulic Explosive Bonding Route
While hydraulic explosive bonding (waterjet-assisted explosion welding) is primarily a solid-state bonding process, thermo-structural coupled analysis contributes in the following ways:
- Post-bonding weld overlay analysis: When hydraulic explosive bonding is used to create the initial clad layer on skirt structures, subsequent weld overlay passes may be required to repair surface defects or add additional cladding layers. Coupled analysis evaluates the interaction between the explosion-bonded interface and subsequent weld thermal cycles.
- Residual stress from explosion bonding: The hydraulic explosive bonding process itself introduces residual stresses at the clad-base metal interface. Coupled analysis characterizes these initial stress states as boundary conditions for subsequent welding operations.
- Structural integrity of bonded skirt assemblies: Analysis validates that the combined effect of explosion bonding residual stresses and weld overlay thermal cycles does not compromise the mechanical integrity of the skirt-to-shell joint.
6.3 Explosion Welding Route
For explosion-welded skirt and shell structures, thermo-structural coupled analysis addresses the following technical challenges:
- Post-explosion weld repair analysis: Explosion welding often produces surface irregularities and local defects that require weld repair. Coupled analysis predicts the residual stress interaction between the explosion-induced stress field and the repair weld thermal cycle.
- Thermal cycling during post-explosion processing: If explosion-welded skirt assemblies require post-weld heat treatment or stress relief, coupled analysis optimizes the thermal cycle to minimize further distortion while effectively reducing residual stresses.
- Multi-process hybrid structures: In complex skirt assemblies where explosion welding creates the primary clad layer and weld overlay provides additional protection at the skirt-shell joint, coupled analysis evaluates the combined residual stress field from both processes.
- Structural qualification: Provides quantitative stress data to support design qualification of explosion-welded skirt structures under applicable pressure vessel codes (ASME BPV Section VIII, GB 150).
7. Validation and Model Verification
7.1 Experimental Validation Methods
Computational predictions from thermo-structural coupled analysis must be validated against experimental measurements to ensure reliability:
| Validation Method | Measured Quantity | Typical Accuracy Target |
|---|---|---|
| Resistance strain gauges | Residual stress at specific points | ±20% of measured value |
| Hole-drilling method (ASTM E837) | Surface residual stress distribution | ±25 MPa |
| X-ray diffraction (ASTM E975) | Bulk residual stress | ±30 MPa |
| Neutron diffraction | Through-thickness residual stress | ±20 MPa |
| Laser displacement measurement | Welding distortion/deformation | ±0.5 mm |
| Thermocouple temperature logging | Thermal cycle parameters | ±10°C |
7.2 Model Verification Protocol
- Perform a coupon-scale welding experiment with full instrumentation (thermocouples, strain gauges, displacement sensors).
- Run the coupled analysis for the identical configuration and compare predictions against measurements.
- Calibrate model parameters (heat source efficiency, boundary condition coefficients) to achieve target accuracy.
- Apply the calibrated model to the full-scale skirt-to-shell structure analysis.
- Document the validation process and accuracy metrics for customer confidence and qualification purposes.
8. Engineering Deliverables and Customer Value
The thermo-structural coupled analysis of skirt-to-shell weld overlay structures generates the following engineering deliverables that directly contribute to customer value:
- Residual stress maps: Detailed contour plots showing stress magnitude and direction throughout the skirt-shell overlay assembly, enabling targeted NDT planning.
- Distortion prediction reports: Quantified predictions of angular and global distortion to support fabrication planning and assembly tolerance management.
- Welding sequence optimization reports: Recommended welding sequences with predicted stress outcomes, reducing trial-and-error during fabrication.
- Structural integrity assessments: Fitness-for-service evaluations demonstrating that overlay-clad skirt structures meet applicable code requirements.
- WPS qualification support documentation: Engineering justification packages that support welding procedure qualification under ASME Section IX, ISO 15614, or NB/T standards.
This analytical capability positions Cladding Technology Shanxi Co., Ltd. as a technically sophisticated provider capable of delivering not only fabrication services but also the engineering intelligence that assures customers of structural integrity, reduces fabrication risk, and minimizes total cost of ownership for overlay-clad pressure vessel support structures.