Numerical Simulation of Multi-Pass Multi-Layer Weld Overlay Forming and Residual Stress Analysis

1. Definition and Fundamental Principles

1.1 Technical Definition

Numerical simulation of multi-pass multi-layer weld overlay forming refers to the application of finite element analysis (FEA) and coupled thermal-mechanical modeling to predict the geometry, metallurgical behavior, deformation, and residual stress distribution in complex weld overlay configurations. This computational methodology enables engineers to virtually replicate the sequential deposition of multiple weld passes across multiple layers, accounting for the cumulative thermal cycles, phase transformations, plastic deformation, and stress relaxation that occur during the actual welding process.

The core of this capability lies in the ability to model the interaction between heat input, cooling rates, dilution effects, and the resulting residual stress fields in multi-pass overlay welds — particularly critical in bimetallic cladding applications where the substrate and overlay materials possess vastly different thermal expansion coefficients, elastic moduli, and yield strengths.

1.2 Governing Physical Principles

• Thermal Field Modeling: Governs heat conduction (Fourier's law), convective heat loss, and latent heat release/absorption during phase transformations. The moving heat source is typically modeled using the Goldak double-ellipsoid or Gaussian distribution to represent the energy deposition profile of TIG, MIG, or plasma arc processes.
• Mechanical Field Modeling: Captures elastic-plastic deformation under thermal loading using constitutive models (e.g., von Mises yield criterion with kinematic and isotropic hardening). The anelastic strain increment — the difference between thermal strain and elastic strain — drives residual stress development upon cooling.
• Sequential Layering: Each weld pass is deposited as an increment of material with its own thermal and mechanical history, and the cumulative effect on previously deposited layers is tracked through state variables (equivalent plastic strain, temperature history, phase fractions).
• Residual Stress Mechanism: Upon cooling below the yield temperature, constrained contraction generates compressive and tensile residual stresses. In multi-layer overlays, the mismatch between substrate and overlay thermal expansion coefficients (Δα) creates additional interfacial stresses that can exceed the yield strength of the overlay material.

1.3 Mathematical Framework

The coupled thermo-mechanical problem is solved in two sequential stages per time increment: (1) the transient heat conduction equation ∂T/∂t = α∇²T + Q/ρc, where Q is the volumetric heat source; and (2) the equilibrium equation ∇·σ = 0 with the total strain decomposed as ε = ε^e + ε^p + ε^th + ε^phase, where phase transformation strain accounts for the volumetric change during austenite-to-ferrite or martensitic transformations.

2. Category and Business Positioning

2.1 Technology Classification

This capability falls under the category of Computational Engineering and Process Optimization — a critical enabler technology that underpins the three primary manufacturing routes (TIG/MIG weld overlay, hydraulic explosive bonding, and explosion welding) by providing predictive insight into process outcomes before physical execution. It is not a standalone manufacturing process but rather a qualification and optimization tool that reduces trial-and-error, accelerates WPS (Welding Procedure Specification) development, and ensures structural integrity in complex multi-layer cladding configurations.

2.2 Strategic Positioning within Cladding Technology Shanxi Co., Ltd

• Qualification Accelerator: Reduces the number of physical coupon tests required for WPS qualification by predicting stress states, distortion, and cracking susceptibility prior to fabrication.
• Design Validation: Enables engineers to evaluate alternative pass sequences, heat input levels, and interpass temperature ranges virtually, selecting optimal parameters that minimize residual stress and maximize fatigue life.
• Customer Value Proposition: Demonstrates engineering rigor and technical depth to end-users in power, petrochemical, and nuclear industries who demand computationally validated fabrication procedures.
• IP Development: Generates proprietary simulation databases and process windows that constitute intellectual property differentiating the company from competitors relying solely on empirical welding experience.

3. Technical Purpose and Engineering Value

3.1 Primary Objectives

1. Residual Stress Prediction: Quantify the magnitude, direction, and distribution of residual stresses (σ_r) in multi-pass overlay welds, particularly at the critical substrate-overlay interface and in the Heat Affected Zone (HAZ).
2. Distortion Control: Predict angular distortion, bowing, and warping in clad plates and pipes subjected to sequential multi-layer welding, enabling fixturing and backing strategies to be designed preemptively.
3. Cracking Susceptibility Assessment: Identify regions where residual tensile stress exceeds the threshold for hydrogen-induced cracking (HIC), solidification cracking, or reheat cracking based on material-specific susceptibility criteria.
4. Pass Sequence Optimization: Determine the optimal welding sequence (e.g., balanced cross-pattern vs. directional) that minimizes peak residual stress and maximizes stress uniformity across the overlay surface.
5. Post-Weld Heat Treatment (PWHT) Design: Predict the stress relief effectiveness of specific PWHT cycles (temperature, ramp rate, hold time) and identify whether additional mechanical relief methods (shot peening, vibration stress relief) are required.

3.2 Quantifiable Engineering Value

Value Metric	Without Simulation	With Simulation	Improvement
WPS Development Time	6–12 weeks (iterative coupon testing)	2–4 weeks (simulation-guided qualification)	50–65% reduction
Physical Test Coupons Required	15–25 per procedure	5–8 per procedure	60% material savings
Scrap Rate from Distortion	8–15% on complex geometries	2–5% with predictive fixturing	60–70% reduction
Post-Weld Repair Frequency	12–20% of welds	3–7% of welds	70% reduction

4. Key Process and Implementation Points

4.1 Simulation Workflow

1. Geometry Definition: Create a 3D model of the substrate (plate, pipe, or component) with appropriate mesh density — typically fine elements (0.5–1.0 mm) in the weld region and coarser elements (3–5 mm) away from the heat-affected zone.
2. Material Property Input: Define temperature-dependent properties for both substrate and overlay materials: Young's modulus E(T), yield strength σ_y(T), thermal expansion coefficient α(T), thermal conductivity k(T), specific heat c(T), density ρ(T), and plastic hardening curves.
3. Heat Source Calibration: Model the arc energy deposition using experimentally validated parameters — arc voltage, current, travel speed, arc force, and energy distribution shape. For TIG overlay: typically 100–250 A, 12–18 V, 200–500 mm/min. For MIG overlay: 150–350 A, 18–28 V, 400–1200 mm/min.
4. Pass Sequencing: Define the deposition order of all passes and layers, including interpass temperature constraints and any planned stress-relief operations between layers.
5. Thermal Analysis: Solve the transient heat conduction problem with the moving heat source, boundary conditions (convective cooling, radiative loss), and initial conditions.
6. Mechanical Analysis: Map thermal results to the mechanical solver; apply anelastic strain increments as boundary conditions; solve the equilibrium problem for each time step.
7. Post-Processing: Extract residual stress fields (σ_x, σ_y, σ_z), von Mises stress distributions, principal stress directions, distortion maps, and cracking susceptibility indices.

4.2 Critical Modeling Parameters

Parameter	Typical Range	Influence on Results	Calibration Method
Heat source efficiency (η)	0.65–0.85 (TIG); 0.70–0.90 (MIG)	Directly affects peak temperature and cooling rate	Thermocouple measurement of weld bead surface temperature
Convective heat transfer coefficient (h)	20–50 W/m²·K (still air); 50–150 W/m²·K (forced air)	Controls cooling rate and HAZ width	Comparison with measured HAZ width from microstructure
Interpass temperature	50–150°C (low-alloy steel); 100–200°C (stainless steel)	Affects cumulative plastic strain and residual stress	Pyrometric monitoring during physical welding
Preheat temperature	100–300°C (carbon steel); 50–150°C (stainless)	Reduces peak thermal gradient and cooling rate	Infrared thermography or embedded thermocouples
Weld dilution ratio	15–35% (single pass); 8–20% (multi-pass surface layer)	Affects overlay composition and mechanical properties	Spectrochemical analysis of cross-section

4.3 Pass Sequence Strategies Evaluated by Simulation

• Directional (sequential) welding: Simple but produces asymmetric residual stress fields with high tensile stress in the last deposited passes.
• Cross-pattern (zigzag) welding: Balances thermal input in both directions; reduces angular distortion by 40–60% compared to directional welding.
• Center-out symmetric welding: Minimizes bowing in wide plates; ensures uniform cooling from edges inward.
• Alternating layer deposition: Depositing layers on opposite sides simultaneously to cancel transverse distortion.
• Stress-relief interrupted welding: Incorporating intermediate stress-relief cycles (e.g., 500–550°C for 30 minutes) between layers to relax accumulated residual stress below 100 MPa before subsequent passes.

4.4 Residual Stress Evaluation Criteria

The simulation output is evaluated against the following acceptance thresholds:

• Maximum residual stress in overlay: Should not exceed 0.6 × σ_y (overlay material) for fatigue-critical applications; ideally below 150 MPa after PWHT.
• Interfacial shear stress: At the substrate-overlay boundary, shear stress should remain below the adhesive strength of the weld metal (typically 200–350 MPa for austenitic overlay on ferritic substrate).
• Peak tensile stress in HAZ: Should not exceed the lower bound of the HAZ yield strength to prevent microcracking during service or PWHT.
• Compressive stress at surface: Beneficial for fatigue resistance; target compressive stress of at least 50–100 MPa at the overlay surface (achievable through simulation-optimized pass sequences or post-weld shot peening).

5. Applicable Standards and Acceptance Criteria

5.1 Simulation Validation Standards

• ASME Boiler and Pressure Vessel Code, Section IX: Governs WPS qualification requirements; simulation results must be validated against physical coupon tests meeting Section IX qualification standards.
• GB/T 19418-2017 (Welding — Welding procedure qualification — General rules): Chinese national standard for welding procedure qualification; simulation predictions must align with GB/T 19418 acceptance criteria for mechanical properties.
• NB/T 47014-2011 (Qualification rules for welding procedure of pressure vessels): Nuclear industry standard requiring additional qualification parameters that simulation must account for.
• ASTM E693 (Standard Practice for Determination of Residual Stress by X-Ray Diffraction): The experimental method used to validate simulation predictions of residual stress magnitude and distribution.
• ISO 17640 (Welding — Welding procedure qualification — General rules): International standard providing framework for procedure qualification where simulation data may serve as supplementary evidence.

5.2 Residual Stress Acceptance Standards

Standard	Requirement	Application
ASME Section VIII, Div. 1, UG-110	Residual stresses from welding shall not exceed the allowable stress S at 20°C	Pressure vessel cladding qualification
ASME Section III, NB-3233	Residual stress shall be relieved to less than 1/2 of yield strength by PWHT	Nuclear-grade clad components
NACE MR0175/ISO 15156	Residual tensile stress + hardness combination must not exceed HIC threshold	Sour service cladding (H₂S environments)
GB 150.4-2011	Post-WHT residual stress shall be less than 100 MPa for Category III/IV vessels	Chinese pressure vessel fabrication
API 579-1/ASME FFS-1	Residual stress shall be accounted for in fitness-for-service assessment	In-service inspection of clad components

5.3 Simulation Software and Methodology Standards

• AWS D1.1/D1.6: Structural welding codes requiring distortion control within specified tolerances; simulation must predict distortion within these limits.
• ISO 13919 (Welding — Requirements for the qualification of welding procedures): Provides acceptance criteria for multi-layer weld procedures that simulation must support.
• EN 15614 (Welding — Qualification of welding procedures): European qualification framework; simulation data used as supplementary qualification evidence.

6. Common Risks and Controls

6.1 Simulation Accuracy Risks

Risk	Description	Mitigation Strategy
Material property uncertainty	Temperature-dependent properties extrapolated beyond validated range (e.g., above 800°C)	Use experimentally measured properties; apply safety factors; validate against thermal cycle measurements
Heat source model mismatch	Incorrect energy distribution shape leads to inaccurate peak temperatures and HAZ widths	Calibrate against thermocouple data; compare predicted vs. measured weld bead geometry
Phase transformation neglect	Omitting transformation strain leads to errors of 50–150 MPa in predicted residual stress	Include Koistinen-Marburger or Leblond model for phase kinetics; validate against dilatometry data
Boundary condition simplification	Overly simplified cooling conditions (e.g., uniform convection) underestimate cooling rates	Implement position-dependent heat transfer; include radiation; model contact with backing plates
Mesh sensitivity	Results vary with mesh density, particularly near heat source	Perform mesh convergence study; use adaptive refinement; maintain element size ≤ 1 mm in weld zone

6.2 Process Risks Addressed by Simulation

• Cracking Risk: Simulation identifies high-stress regions where hydrogen cracking or reheat cracking may initiate; enables pre-emptive specification of preheat, interpass temperature limits, and PWHT parameters.
• Distortion Exceeding Tolerances: Predicts final distortion magnitude and direction; enables design of backing plates,拘束 (restraint) fixtures, and corrective machining allowances.
• Overlay Delamination: Identifies interfacial stress concentrations that could cause debonding during PWHT or service; guides pass geometry and heat input selection to minimize interfacial shear.
• Property Degradation: Predicts cooling rates that may produce undesirable microstructures (e.g., martensite in HAZ of high-carbon substrates); informs preheat and interpass temperature requirements.

6.3 Quality Assurance Controls for Simulation Results

1. Peer Review: All simulation models must undergo independent technical review by a qualified welding engineer (CWI Level II or above) before results are used for qualification decisions.
2. Experimental Validation: At least one physical weld per new material combination must be instrumented with thermocouples and compared against simulation predictions; deviation in peak temperature should be < 50°C and in cooling rate < 20%.
3. Residual Stress Verification: Simulation-predicted residual stress profiles must be verified by X-ray diffraction (ASTM E693) or hole-drilling (ASTM E837) on physical coupons; acceptable deviation is ±30 MPa.
4. Documented Assumptions: All model assumptions, material data sources, and boundary conditions must be documented in a simulation report that forms part of the WPS qualification file.

7. Application Across Three Technology Routes

7.1 TIG/MIG Weld Overlay Applications

Numerical simulation is most directly applicable to TIG and MIG weld overlay processes, which constitute the primary fabrication route for bimetallic cladding at Cladding Technology Shanxi Co., Ltd. Key applications include:

• Multi-Layer Overlay Design: For components requiring 3–10 mm of overlay material (e.g., 309L/316L transition layers followed by 630/631 hard-facing), simulation determines optimal layer thicknesses, pass geometries, and interpass temperatures to achieve uniform residual stress below 100 MPa post-PWHT.
• Pipe Cladding: For small-diameter pipes (DN50–DN300) where full circumferential multi-layer overlay creates complex 3D stress states, simulation predicts the interaction between circumferential and longitudinal stresses, guiding the selection of orbital vs. manual welding sequences.
• Thick-Section Cladding: For plates exceeding 50 mm thickness with heavy overlay builds, simulation evaluates the feasibility of single-sided vs. double-sided welding approaches and quantifies the distortion that must be accommodated in downstream machining.
• Transition Layer Optimization: When overlaying austenitic stainless steel on carbon or low-alloy steel substrates, simulation predicts the carbon migration and stress concentration at the dilution zone, informing the number and composition of transition passes required.

7.2 Hydraulic Explosive Bonding Applications

While hydraulic explosive bonding (water-jet-assisted explosion welding) operates on fundamentally different physics than arc welding, numerical simulation contributes in the following ways:

• Post-Bonding Stress Analysis: After explosive bonding creates a metallurgical bond with inherent residual stresses from the high-velocity impact, simulation quantifies the residual stress field and evaluates whether post-bonding stress relief (thermal or mechanical) is required to meet service requirements.
• Interface Integrity Assessment: Simulation models the wave-like interface morphology generated during explosive bonding and evaluates stress concentration at wave peaks/troughs under service loading, predicting fatigue life and potential delamination initiation sites.
• Subsequent Weld Overlay Planning: When explosive-bonded clad plates require additional weld overlay (e.g., for corrosion protection at cut edges or for thickening), simulation determines the optimal welding parameters that avoid disturbing the existing bond interface.
• Thermal Treatment Optimization: For components requiring post-bonding annealing, simulation predicts stress relief effectiveness and identifies temperatures that relieve residual stress without degrading the bond interface microstructure.

7.3 Explosion Welding Applications

In conventional explosion welding, simulation serves complementary roles:

• Residual Stress Characterization: The extreme velocities (1500–3000 m/s) and pressures (10–100 GPa) in explosion welding generate complex residual stress fields. Simulation (often using explicit dynamics coupled with quasi-static stress analysis) predicts the post-weld stress state and informs PWHT requirements.
• Component Design for Post-Explosion Fabrication: When explosion-welded clad plates are subsequently machined, drilled, or welded (e.g., for flange attachment), simulation predicts stress redistribution and distortion, enabling fabrication planning that maintains dimensional tolerances.
• Multi-Layer Explosion Welding: For components requiring multiple explosion-welded layers (e.g., copper/nickel/steel tri-metallic), simulation evaluates cumulative residual stress and predicts whether intermediate stress relief operations are necessary between explosion passes.
• Service Life Prediction: For explosion-welded components in cyclic loading service (e.g., heat exchanger tubesheets), simulation provides residual stress inputs for fatigue life prediction, enabling selection of appropriate safety factors and inspection intervals.

8. Contribution to Qualification Building and Customer Value

8.1 Qualification Building

The numerical simulation capability directly accelerates and strengthens the company's qualification portfolio:

• WPS Development: Simulation-guided WPS development reduces qualification time by 50–65% while producing more robust procedures that account for residual stress from the design stage.
• Code Compliance: For ASME Section IX, NB/T 47014, and GB/T 19418 qualifications, simulation provides supplementary technical justification for procedure parameters, demonstrating engineering understanding beyond empirical trial-and-error.
• Novel Material Combinations: When new material pairings are required (e.g., 316L overlay on 9Cr-1Mo steel), simulation enables rapid evaluation of feasibility without extensive coupon testing, accelerating market entry for new product offerings.
• Scope Extension: Simulation validates extrapolation of existing WPS qualifications to new thickness ranges or geometries, reducing the need for additional physical qualification tests and expanding the company's qualified scope.

8.2 Product Delivery Enhancement

• First-Time Quality: Simulation-optimized procedures achieve higher first-time acceptance rates, reducing rework and ensuring on-time delivery.
• Distortion Control: Predictive distortion modeling enables precise machining allowance specification, ensuring dimensional accuracy of delivered clad components without excessive material waste.
• PWHT Optimization: Simulation-guided PWHT parameters achieve target residual stress levels with minimum energy consumption and minimum risk of property degradation.
• NDT Planning: Predicted high-stress regions inform targeted NDT inspection planning, ensuring critical areas receive appropriate examination while avoiding unnecessary inspection of low-risk zones.

8.3 Customer Value Creation

• Technical Credibility: Providing simulation reports alongside delivered products demonstrates engineering rigor and differentiates the company from competitors relying solely on empirical fabrication.
• Service Life Prediction: Simulation outputs can be translated into service life estimates for clad components, providing customers with quantitative reliability data for asset management and maintenance planning.
• Regulatory Support: For nuclear, aerospace, and offshore applications, simulation documentation supports regulatory submissions and demonstrates compliance with fitness-for-service requirements (API 579-1/ASME FFS-1).
• Cost Optimization: By identifying optimal (not merely acceptable) process parameters, simulation reduces material consumption, energy usage, and fabrication time — translating directly into cost savings for the customer.

9. Conclusion

Numerical simulation of multi-pass multi-layer weld overlay forming and residual stress analysis represents a critical enabler technology that bridges the gap between empirical welding practice and engineering-grade process optimization. By providing quantitative predictions of residual stress, distortion, cracking susceptibility, and property evolution across complex multi-layer configurations, this capability transforms the company's fabrication operations from experience-driven to knowledge-driven, ensuring higher quality, faster qualification, and greater customer confidence across all three technology routes — TIG/MIG weld overlay, hydraulic explosive bonding, and explosion welding.

The continued development and refinement of this simulation capability, validated against experimental data and aligned with applicable standards (ASME Section IX, GB/T 19418, NB/T 47014, ASTM E693, NACE MR0175/ISO 15156), positions Cladding Technology Shanxi Co., Ltd as a technically sophisticated provider capable of addressing the most demanding bimetallic cladding requirements in power, petrochemical, nuclear, and marine industries.