Welding Temperature Field and Deformation Numerical Simulation for Bimetallic Cladding Process Optimization

1. Definition and Fundamental Principles

Welding temperature field and deformation numerical simulation is a computational engineering methodology that employs finite element analysis (FEA) tools—principally Sysweld, Simufact Welding, and complementary FEA platforms—to predict and visualize the transient thermal history, cooling rate (cooling velocity), residual stress distribution, and geometric deformation that occur during weld overlay, explosive bonding, and hydraulic explosive bonding processes. The core principle rests on solving coupled thermo-mechanical partial differential equations governing heat conduction, thermal expansion, plastic deformation, and material phase transformation under the highly localized and rapidly fluctuating thermal loads characteristic of welding and impact-bonding operations.

In the context of bimetallic cladding manufacturing, numerical simulation serves as a virtual rehearsal environment. Before any physical trial is conducted, engineers can model the complete process sequence—including multi-pass weld overlay schedules, interpass temperature profiles, cooling strategies, and post-weld thermal treatment (PWHT) cycles—to predict the resulting metallurgical and mechanical outcomes. This eliminates reliance on iterative physical trial-and-error, which is particularly costly when dealing with expensive alloy consumables, large-format clad plates, or thick-walled clad pipes requiring extensive preheating and cooling infrastructure.

1.1 Governing Physics

The simulation framework typically integrates the following physical phenomena:

Transient heat conduction: Modeled via the Fourier heat equation with source terms representing the welding arc, explosive energy release, or hydraulic shock loading. The heat input is characterized by parameters such as arc power, travel speed, electrode diameter, and current type (DC/AC).
Thermoelastic-plastic deformation: The material response to thermal gradients is computed using constitutive models that account for elastic, plastic, and creep behavior at elevated temperatures. Material properties (yield strength, elastic modulus, thermal expansion coefficient) are defined as temperature-dependent functions.
Phase transformation modeling: For steels susceptible to martensitic transformation, the Kolmogorov-Johnson-Mehl-Avrami (KJMA) equation or Scheil solidification model is often incorporated to capture volume changes and stress redistribution associated with phase changes during solidification and cooling.
Residual stress accumulation: The incremental plastic deformation approach (e.g., the Goldak or modified Goldak source model) captures the cumulative residual stress field resulting from sequential heat cycles in multi-pass overlay welding.

1.2 Software Platforms

The company utilizes two primary commercial simulation platforms, each with distinct strengths:

Platform	Core Strength	Typical Application in Cladding
Sysweld	Dedicated welding process simulation; highly refined thermal-mechanical coupling for arc welding	Multi-pass weld overlay sequence optimization; interpass temperature control; residual stress prediction in thick clad plates
Simufact Welding	Integrated process chain simulation (welding + forming + PWHT); robust meshing and remeshing algorithms	Full process chain from weld overlay through post-weld heat treatment; distortion prediction for large structural assemblies; cooling strategy evaluation
General FEA (Abaqus, ANSYS)	Custom constitutive models; high-fidelity material behavior; explosion/explosive bonding energy modeling	Explosion welding impact dynamics; hydraulic explosive bonding pressure wave analysis; custom phase transformation models

2. Category and Business Positioning

This technology is classified under the company's Process Temperature Control and Cooling major category, within the Simulation Prediction technical direction, and serves the strategic purpose of Process Pre-Optimization. It is designated for R&D and New Product Introduction activities.

Within the company's overall process engineering framework, numerical simulation occupies a critical upstream position in the development pipeline. It functions as the intellectual foundation upon which all subsequent physical trial work, WPS qualification, and production scaling are built. By shifting the optimization burden from the physical shop floor to the computational environment, the company achieves the following business objectives:

Reduction of trial-and-error costs: Each physical weld overlay trial on expensive alloy materials (e.g., Hastelloy C-276, Stellite 6, Inconel 625) incurs significant material, labor, and equipment costs. Simulation pre-screening eliminates ineffective parameter combinations before any physical trial is conducted.
Acceleration of new product introduction timelines: For novel clad configurations (new base metal/cladding alloy combinations, new geometries, new thickness ratios), simulation enables rapid evaluation of multiple process variants in compressed calendar time.
Enhanced qualification credibility: Simulation results provide a physics-based justification for selected process parameters, strengthening WPS/PQR documentation and customer confidence during qualification audits.
Knowledge retention and transfer: Simulation models encapsulate process know-how in a reproducible, version-controlled digital format, reducing dependence on individual welder or engineer experience.

3. Technical Purpose and Value

3.1 Primary Technical Objectives

Temperature field prediction: Determine the peak temperature, thermal gradient, and cooling rate (particularly the t₈₀₀ cooling time from 800°C to 600°C) at every point in the clad component. This is critical for predicting microstructural evolution, hardness distribution, and susceptibility to cracking.
Cooling rate optimization: Identify regions where cooling rates exceed critical thresholds for hydrogen-induced cracking (HIC) or cold cracking, and design cooling strategies (controlled cooling, back-heat application, insulating blankets) to mitigate these risks.
Residual stress mapping: Predict the magnitude and distribution of residual stresses, particularly transverse and longitudinal stresses near the weld/overlay interface, to assess risks of distortion, stress corrosion cracking (SCC), and fatigue life degradation.
Deformation and distortion prediction: Quantify out-of-plane warping, angular distortion, and overall dimensional changes to design compensatory fixtures, tacking sequences, and post-weld straightening requirements.
Process sequence rehearsal: Evaluate alternative weld pass sequences, tack weld patterns, and cooling interventions virtually to identify the optimal sequence before committing to physical execution.

3.2 Quantifiable Value

Industry benchmarks and internal experience indicate that systematic use of welding simulation can reduce the number of physical trial cycles by 40–70% for new process developments. For a typical large-format clad plate qualification involving 300 mm thickness base plate with multi-layer weld overlay, this translates to savings of several weeks of calendar time and hundreds of thousands of RMB in material and processing costs per project.

4. Key Process and Implementation Points

4.1 Simulation Workflow

The standard implementation workflow follows a structured, iterative methodology:

Geometric modeling and meshing: Create a CAD model of the clad component with appropriate geometric detail. Apply boundary conditions representing fixturing, clamping, and environmental conditions. Generate a finite element mesh with element sizes refined in the weld zone (typically 1–3 mm in the heat-affected zone, coarser in the far-field).
Material property definition: Input temperature-dependent thermophysical properties (density, specific heat, thermal conductivity, thermal expansion coefficient, elastic modulus, yield strength, Poisson's ratio) for both base metal and cladding alloy. For phase-transforming materials, define transformation temperature ranges and associated volumetric changes.
Heat source model configuration: Select and calibrate the appropriate heat source model. For TIG/MIG weld overlay, use the Goldak double-ellipsoid or conical heat source model, calibrated against measured bead geometry and thermal cycle data. For explosion welding, model the impact energy as a prescribed velocity boundary condition or pressure pulse.
Process sequence definition: Define the welding sequence, including pass order, travel speed, current/voltage parameters, interpass temperature constraints, and any cooling interventions (back-heat, water quench, controlled cooling blankets). For multi-layer overlay, define each layer's deposition geometry and schedule.
Simulation execution and post-processing: Run the transient thermal-mechanical analysis. Post-process results to extract temperature histories, cooling rate maps, residual stress contours, and deformation profiles. Compare key metrics against acceptance criteria and qualification requirements.
Iterative optimization: Adjust process parameters based on simulation findings—modify interpass temperature limits, add or relocate tack welds, alter pass sequence, introduce back-heat, or modify cooling strategy. Re-run simulations until all criteria are satisfied.

4.2 Critical Simulation Parameters for Weld Overlay

Parameter	Typical Range (TIG Overlay)	Typical Range (MIG Overlay)	Sensitivity
Arc current	80–200 A	150–350 A	High
Travel speed	30–80 mm/min	100–300 mm/min	High
Heat input (kJ/mm)	0.5–2.5	1.5–6.0	Very High
Interpass temperature	80–200°C (material-dependent)	100–250°C (material-dependent)	High
Preheat temperature	100–300°C (depending on base material)	100–300°C	Medium
Shielding gas	Ar or Ar/He mix	Ar/CO₂ mix or pure Ar	Low (thermal effect)
Number of overlay passes	2–15 (depending on clad thickness)	2–8	High

4.3 Key Output Metrics and Acceptance Thresholds

Output Metric	Typical Acceptance Criterion	Relevance to Cladding Quality
Cooling time t₈₀₀ (800→600°C)	> 10 s for low-alloy steels; > 20 s for Cr-Mo steels (adjust per material)	Prevents cold cracking and hard martensitic transformation in HAZ
Peak interpass temperature	Below material-specific limit (e.g., < 250°C for duplex SS overlay)	Prevents grain coarsening, phase imbalance in duplex, and sensitization
Residual stress (longitudinal)	< 0.5 × yield strength of base metal (or below SCC threshold)	Reduces risk of stress corrosion cracking in cladding layer
Residual stress (transverse)	< 0.3 × yield strength (or below cracking threshold)	Prevents transverse cracking at weld/overlay interface
Maximum out-of-plane distortion	Within ±1.5 mm/m or per drawing tolerance	Ensures dimensional conformance for downstream fabrication
Angular distortion	Within specified tolerance (typically < 2°)	Maintains flatness and parallelism of clad surfaces

4.4 Cooling Strategy Optimization

Cooling strategy design is one of the most impactful applications of numerical simulation in weld overlay processes. The simulation enables engineers to evaluate the following cooling interventions virtually:

Controlled cooling with insulation blankets: Simulate the thermal mass and insulation properties of ceramic fiber or steel wool blankets to extend cooling times and reduce cooling rates in critical zones.
Back-heat application: Model the placement, power, and duration of induction or resistance back-heat units to maintain a minimum temperature in the HAZ during multi-pass overlay.
Active water cooling: For processes where rapid cooling is desired (e.g., certain austenitic stainless steel overlays where controlled cooling promotes desired grain structure), simulate the cooling rate achieved by directed water spray or immersion cooling.
Post-weld thermal treatment (PWHT) cycles: Model the stress relief and aging cycles to predict residual stress reduction, microstructural stabilization, and any additional distortion from thermal cycling.

5. Applicable Standards and Acceptance Criteria

While numerical simulation itself is not directly governed by a single standard, the outputs and process parameters derived from simulation must align with the following standards and specifications:

5.1 Welding Process and Qualification Standards

GB/T 19418 (Welding — Welding procedure qualification): Defines the requirements for WPS/PQR that simulation-optimized parameters must ultimately satisfy.
ASME BPVC Section IX: Governs welding procedure qualification for pressure vessel applications; simulation-derived parameters must fall within qualified essential variables.
ASTM A403 / A240 / A213: Material specifications for clad components; simulation must predict thermal histories compatible with material requirements.
API 578 (Qualification of Welding Inspectors): While not directly applicable to simulation, the qualification framework ensures that simulation-informed processes are inspected and verified by qualified personnel.
ISO 15614 (Qualification of welding procedures for metallic materials): International qualification framework requiring documented process parameters that simulation helps optimize.

5.2 Non-Destructive Testing and Inspection Standards

GB/T 3323 (Radiographic testing of welds): Simulation-predicted weld geometry and penetration inform radiographic inspection planning.
GB/T 11345 (Ultrasonic testing of welds): Residual stress and deformation predictions guide UT scan strategy and acceptance criteria interpretation.
NB/T 47013 (Non-destructive testing for pressure equipment): Series of standards governing NDT methods for pressure vessel clad components.
ASME BPVC Section V: Acceptance criteria for NDT methods used to verify simulation-predicted outcomes.

5.3 Thermal and Metallurgical Standards

GB/T 6393 (Determination of hardness of welds in steel): Hardness profiles predicted by simulation (via cooling rate and phase transformation models) are verified against this standard.
ASTM E10 / E92 (Rockwell/Vickers hardness testing): Standard methods for validating simulation-predicted hardness distributions.
NACE MR0175 / ISO 15156 (Materials for H₂S environments): For clad components in sour service, simulation must ensure cooling rates and residual stresses are compatible with HIC/SOHIC resistance requirements.
ASME Section II, Part D (Properties of Materials for Construction): Material property data used in simulation must conform to these specifications.

5.4 Simulation-Specific Standards and Guidelines

ASME V&V 10-2006 (Standard for Verification and Validation in Computational Solid Mechanics): Provides framework for validating simulation models against physical test data.
ISO 17123 (Coordinate measurement machines): Relevant for measuring physical distortion to validate simulation predictions.
ISO 9001:2015 (Quality management systems): Requires documented evidence of process control, including simulation-based optimization records.

6. Common Risks and Controls

Risk	Description	Control Measures
Material property inaccuracy	Temperature-dependent material properties in the simulation database may not accurately represent the specific alloy grade or heat treatment condition used in production	Validate material properties against coupon test data from the actual production batch; perform sensitivity analysis on key properties; update property curves based on measured thermal cycle data
Heat source model mismatch	The mathematical heat source model may not accurately represent the actual energy deposition pattern of the welding process	Calibrate heat source parameters against measured bead geometry, penetration, and thermal cycle data from coupon tests; use multiple heat source models and compare predictions
Boundary condition oversimplification	Fixturing, clamping, and environmental conditions may be oversimplified, leading to inaccurate deformation predictions	Model actual production fixturing with measured stiffness values; include convective and radiative heat loss at realistic coefficients; validate with physical strain gauge measurements
Mesh sensitivity	Results may vary significantly with mesh density and element type, leading to unreliable predictions	Perform mesh convergence studies; use adaptive remeshing in the weld zone; maintain minimum element size criteria in the HAZ
Phase transformation model uncertainty	Phase transformation kinetics (especially for low-alloy and Cr-Mo steels) may be poorly characterized, leading to errors in residual stress prediction	Use experimentally calibrated transformation models (e.g., dilatometry data); include transformation plasticity effects; validate against measured residual stress data
Over-reliance on simulation	Excessive trust in simulation results without physical validation may lead to process failures in production	Always validate simulation predictions against physical trial data for critical processes; maintain a documented correlation between simulation and physical results; use simulation for optimization, not sole qualification
Interpass temperature drift	Actual interpass temperatures during production may deviate from simulated values due to environmental factors, operator variation, or scheduling delays	Implement real-time temperature monitoring with automated interpass temperature alarms; define acceptable temperature windows in the WPS; train operators on interpass temperature control

7. Application Scenarios Across Company Technology Routes

7.1 TIG/MIG Weld Overlay Route

Weld overlay is the primary application domain for temperature field and deformation simulation. The following specific scenarios illustrate the value of simulation in this route:

Multi-layer, multi-pass overlay on thick base plates: For clad plates with overlay thicknesses of 6–25 mm (common in pressure vessel and heat exchanger applications), simulation is essential to optimize the pass sequence, interpass temperature limits, and cooling strategy. Without simulation, the residual stress accumulation and distortion from 8–15 sequential weld passes on a thick section would be unpredictable, leading to excessive trial-and-error. Simulation enables the identification of optimal pass sequences (e.g., symmetric vs. sequential, balanced vs. unbalanced) that minimize angular distortion and residual stress.

Sensitization control in austenitic stainless steel overlays: For overlays using materials such as 309L, 310L, or Inconel 625 on carbon steel or low-alloy steel bases, the thermal cycle directly influences sensitization (chromium carbide precipitation) in the HAZ. Simulation predicts the time spent in the sensitization temperature range (450–850°C), enabling optimization of interpass temperature and cooling rate to minimize sensitization risk. This is particularly critical for applications governed by NACE MR0175 / ISO 15156 where intergranular corrosion resistance is paramount.

Duplex stainless steel overlay process control: Duplex stainless steel (e.g., 2205, 2507) overlays are highly sensitive to thermal history, which controls the ferrite/austenite phase balance. Simulation predicts the cooling rate and peak temperature at each point in the overlay, enabling optimization of the process to maintain the phase balance within the acceptable range (typically 35–65% ferrite per ASTM A240 / EN 10216-5). This prevents excessive ferrite (which increases pitting susceptibility) or excessive austenite (which reduces strength and SCC resistance).

Clad pipe welding and repair simulation: For clad pipes (e.g., API 5L X70 with 309L/316L overlay), simulation predicts the thermal cycle and residual stress distribution around the weld joint, including the overlay layer. This is critical for ensuring that the weld does not compromise the corrosion resistance of the cladding layer and that residual stresses are below the SCC threshold for the specific service environment.

7.2 Hydraulic Explosive Bonding Route

While hydraulic explosive bonding (HEB) differs fundamentally from arc welding in its energy source (hydrodynamic shock vs. electrical arc), numerical simulation remains a critical tool for process optimization:

Impact velocity and bonding quality prediction: Simulation models the hydrodynamic impact dynamics to predict the local impact velocity at the bonding interface. The critical bonding velocity (typically 2–6 m/s for most metal pairs) must be achieved without exceeding the material's fracture velocity. Simulation enables optimization of explosive charge geometry, water column pressure, and plate configuration to achieve the target impact velocity uniformly across the bonding area.

Post-bond residual stress and deformation: The explosive impact generates significant plastic deformation and residual stresses in both the base and cladding plates. Simulation predicts the magnitude and distribution of these residual stresses, which directly affect the mechanical performance of the bonded joint. For applications requiring high residual stress levels (e.g., shot peening-equivalent surface compressive stresses for fatigue resistance), simulation helps optimize the process parameters to achieve the desired stress state.

Temperature rise during impact: Although HEB is generally considered a "cold" bonding process, the adiabatic shear deformation at the bonding interface can cause localized temperature rises. Simulation predicts these temperature peaks, which are critical for understanding the metallurgical bonding mechanism (adiabatic shear instability, jet formation, oxide disruption) and ensuring that the temperature does not exceed limits that would compromise the cladding material's properties.

7.3 Explosion Welding Route

Explosion welding (EW) is the most energy-intensive of the company's three bonding routes, and simulation plays an even more critical role due to the complexity of the process:

Explosive charge design and detonation modeling: Simulation models the detonation wave propagation, gas expansion, and plate acceleration to predict the impact velocity, impact angle, and collision geometry. This enables optimization of explosive charge weight, detonator placement, and stand-off distance to achieve uniform bonding across the entire plate area. For large-format plates (e.g., 2000 × 3000 mm), simulation is essential to ensure that the impact conditions are consistent across the full surface area.

Post-explosion deformation and residual stress: The explosive energy generates significant plastic deformation in both plates, particularly at the impact zone. Simulation predicts the final geometry (including any permanent deformation or "mushrooming" at the impact edges) and the residual stress field. This information is critical for downstream processing (e.g., trimming, machining, PWHT) and for ensuring that the bonded plate meets dimensional and mechanical requirements.

Thermal effects in high-energy explosion welding: For thick plates or high-energy explosive charges, the plastic deformation energy can cause significant temperature rises in the plates. Simulation predicts these thermal histories, which may require PWHT to relieve residual stresses and stabilize microstructures. The cooling rate predictions from simulation inform the design of post-explosion cooling strategies to prevent cracking or microstructural degradation in the cladding layer.

8. Contribution to Qualification Building and Customer Value

8.1 WPS Qualification Support

Simulation-derived process parameters provide a physics-based justification for the essential variables selected in the Welding Procedure Specification (WPS). During WPS qualification under ASME Section IX, ISO 15614, or GB/T 19418, the following simulation outputs strengthen the qualification documentation:

Thermal cycle predictions demonstrating that interpass temperatures and cooling rates are within qualified ranges
Residual stress maps showing that stress levels are below cracking and SCC thresholds
Deformation predictions confirming that dimensional tolerances will be met after welding
Optimized pass sequences that minimize the number of welding operations while maintaining quality

8.2 New Product Introduction Acceleration

For new clad configurations (novel alloy combinations, new geometries, new thickness ratios), simulation enables rapid evaluation of multiple process variants without committing to physical trials. This accelerates the new product introduction (NPI) timeline by:

Identifying the most promising process parameters for physical trial within days rather than weeks
Reducing the number of physical trials required to achieve a qualified process
Providing predictive data for design reviews and customer presentations
Enabling "what-if" analysis for process modifications requested by customers

8.3 Customer Value and Competitive Advantage

The application of numerical simulation in cladding process development delivers measurable customer value:

Reduced time-to-market: Faster qualification and production ramp-up for new clad products
Improved first-pass yield: Simulation-optimized processes have higher success rates on first physical trial, reducing scrap and rework
Enhanced product reliability: Predicted residual stress and deformation profiles enable proactive quality assurance, reducing field failures and warranty claims
Customized process solutions: Simulation enables tailored process development for specific customer requirements (e.g., specific cooling rate ranges, residual stress limits, or dimensional tolerances)
Documentation and traceability: Simulation records provide a complete digital history of process development decisions, supporting quality audits and regulatory compliance

9. Implementation Recommendations

9.1 Model Validation Protocol

Every simulation model used for process optimization must undergo a documented validation protocol:

Develop a physical coupon test program that replicates the simulated process conditions
Instrument coupons with thermocouples, strain gauges, and displacement sensors to capture thermal cycles, strain histories, and deformation
Compare simulation predictions against measured data for key outputs (temperature, cooling rate, residual stress, deformation)
Document the correlation accuracy and define acceptable deviation thresholds
Update the simulation model's material properties, heat source parameters, and boundary conditions based on validation results
Archive the validated model and validation data for future reference and audit

9.2 Continuous Improvement Cycle

Simulation should be treated as a living tool that improves with each project:

Maintain a library of validated material property sets for all alloy grades used in production
Archive simulation models and results for each qualified WPS to enable rapid reuse and modification
Conduct post-project reviews comparing simulation predictions against actual production outcomes
Incorporate lessons learned from production deviations into model updates
Invest in continuous training of simulation engineers on new software capabilities and advanced modeling techniques

9.3 Integration with Digital Manufacturing

The long-term strategic direction for numerical simulation in the company's cladding operations should include:

Integration of simulation models with digital twin platforms for real-time process monitoring and adaptive control
Development of surrogate models (machine learning-based) trained on simulation data for rapid parameter optimization during production
Integration of simulation outputs with NDT planning tools to optimize inspection strategy based on predicted defect susceptibility zones
Development of standardized simulation workflows for common clad configurations to reduce model development time for repeat orders

10. Conclusion

Welding temperature field and deformation numerical simulation is an indispensable capability for any organization engaged in high-integrity bimetallic cladding manufacturing. By providing physics-based predictions of thermal history, cooling rate, residual stress, and geometric deformation, simulation transforms the process development workflow from an empirical trial-and-error exercise into a rational, predictive engineering discipline. For Cladding Technology Shanxi Co., Ltd., this capability directly supports the company's three technology routes—TIG/MIG weld overlay, hydraulic explosive bonding, and explosion welding—by enabling process pre-optimization, reducing qualification costs, accelerating new product introduction, and delivering enhanced product quality and reliability to customers. The systematic implementation of simulation, supported by rigorous model validation and continuous improvement, positions the company at the forefront of digital manufacturing in the bimetallic cladding industry.