Weld Penetration Depth Prediction via Variable-Speed GTAW Temperature Field Modeling

1. Definition and Fundamental Principles

The research study titled "Weld Penetration Depth Prediction Based on Variable-Speed GTAW Welding Temperature Field Analysis Model" represents a critical analytical capability within Cladding Technology Shanxi Co., Ltd.'s technical infrastructure. This work addresses one of the most persistent engineering challenges in Gas Tungsten Arc Welding (GTAW) overlay fabrication: the accurate prediction of weld penetration depth under dynamic, non-steady-state thermal conditions.

In conventional GTAW overlay welding, the weld pool geometry—including penetration depth, cap width, and fusion boundary—is governed by a complex interplay of heat input, travel speed, arc force, and material thermal properties. When the travel speed varies during a production run (as is common in multi-pass overlay sequences, contour welding, or repair operations), the thermal field becomes transient, and steady-state analytical models lose accuracy. The variable-speed GTAW temperature field analysis model developed under this study captures these transient thermal dynamics by solving the heat conduction equation with moving heat sources whose intensity and position evolve in time and space.

1.1 Governing Thermal Physics

The model is rooted in the three-dimensional transient heat conduction equation:

ρC_p(∂T/∂t) = k_x(∂²T/∂x²) + k_y(∂²T/∂y²) + k_z(∂²T/∂z²) + Q(x,y,z,t)

Where ρ is material density, C_p is specific heat capacity, k is thermal conductivity (which may be temperature-dependent), and Q represents the volumetric heat source distribution. The Rosenthal heat source model is extended to accommodate variable travel velocity v(t), which directly influences the asymmetry of the thermal field and, consequently, the penetration profile.

1.2 Variable-Speed Effect on Penetration

At constant travel speed, the thermal field reaches a quasi-steady state after a short transient period, and penetration depth stabilizes. When travel speed varies—accelerating or decelerating—the thermal accumulation in the weld zone changes dynamically:

• Deceleration zones: Heat input per unit length increases, leading to deeper penetration and wider fusion zones. This can be exploited for keyhole formation in multi-pass builds or may cause excessive dilution in overlay applications.
• Acceleration zones: Reduced heat input per unit length leads to shallower penetration and narrower welds, potentially causing incomplete fusion at the fusion boundary.
• Turn-around and stop-start points: Thermal accumulation is maximized, creating localized deep penetration that must be accounted for in overlay layer thickness control.

2. Category and Business Positioning

This research study falls squarely within the company's TIG/MIG Weld Overlay Technology Route and serves as a foundational analytical tool that bridges theoretical metallurgy with production execution. It is positioned as a process engineering knowledge asset—a capability that elevates the company from empirical, experience-driven overlay welding to model-informed, predictive manufacturing.

2.1 Role in the Company's Technical Ecosystem

Within Cladding Technology Shanxi Co., Ltd.'s three technology routes:

• TIG/MIG Weld Overlay: This is the primary beneficiary. The penetration depth prediction model directly informs WPS parameter selection, multi-pass sequence planning, and overlay dilution control. It enables the engineering team to predict how travel speed variations—whether intentional (e.g., weave patterns, contour following) or incidental (e.g., manual operator variation)—affect the final overlay geometry and metallurgical quality.
• Hydraulic Explosive Bonding: Indirect contribution. While explosive bonding does not involve welding, the penetration prediction model informs the design of post-bonding weld overlay layers that may be applied to bonded assemblies (e.g., overlaying a corrosion-resistant cap layer on an explosion-bonded substrate).
• Explosion Welding: Similar indirect contribution. When explosion-welded clad plates require additional weld overlay for thickness build-up or repair, the temperature field model guides the overlay process design to avoid damaging the existing explosive bond interface.

3. Technical Purpose and Value

3.1 Primary Technical Objectives

1. Predictive Penetration Control: Enable the engineering team to calculate expected weld penetration depth for any given combination of current (I), voltage (V), travel speed (v), wire feed rate, and gas shielding conditions—without requiring physical trial welds for every parameter variation.
2. Dilution Rate Estimation: Predict the base metal dilution percentage in each overlay pass, which is critical for maintaining the required corrosion resistance or wear resistance of the final clad surface per specifications such as ASTM A240, NACE MR0175, or ASME B31.3.
3. Multi-Pass Sequence Optimization: Determine the optimal number of passes, interpass travel speed profiles, and heat input distribution to achieve target overlay thickness with minimal dilution and controlled residual stress.
4. Non-Steady-State Process Understanding: Provide a theoretical basis for managing penetration variation at weld starts, stops, and transitions between straight sections and contours.

3.2 Business Value

• Reduced Trial-and-Error Costs: Each physical trial weld on expensive alloy materials (Inconel, Hastelloy, Stellite, 309L, 316L) consumes consumables, machine time, and NDT resources. The model reduces the number of qualification trials by providing a pre-screened parameter window.
• Accelerated WPS/PQR Development: When developing a new Welding Procedure Specification (WPS) for a specific substrate-overlay combination, the model narrows the parameter range, reducing the number of Procedure Qualification Records (PQR) required under ASME Section IX or ISO 15614-1.
• Customer Confidence: Demonstrating a rigorous analytical capability—beyond empirical rule-of-thumb—strengthens the company's technical credibility in competitive bids for high-integrity applications in oil & gas, power generation, and chemical processing.
• Operator Training Enhancement: The model provides a quantitative framework for training welders on how their travel speed control affects weld geometry, moving training from purely observational to physics-based.

4. Key Process and Implementation Points

4.1 Model Inputs and Parameter Matrix

The variable-speed GTAW temperature field model requires the following input parameters. The table below summarizes typical ranges and their influence on penetration depth:

Parameter	Symbol	Typical Range (Overlay Applications)	Effect on Penetration
Welding Current	I	80–350 A	Increasing I increases penetration depth approximately linearly (P ∝ I1.5 in many regimes)
Welding Voltage	V	10–25 V	Higher V indicates larger arc column; moderate effect on penetration
Travel Speed (Variable)	v(t)	30–150 mm/min	Penetration inversely proportional to v; P ∝ 1/v in quasi-steady state
Wire Feed Rate	WFR	0.5–3.0 m/min (if GTAW with filler)	Indirect: affects dilution and cap geometry more than root penetration
Shielding Gas Composition	—	Ar, Ar+2%O₂, Ar+5%CO₂	Affects arc stability and heat concentration; O₂ addition can increase penetration
Interpass Temperature	Tip	≤ 150°C (typical max)	Higher Tip reduces thermal gradient, slightly increases dilution
Tungsten Electrode Diameter	de	1.6–4.0 mm	Larger electrode supports higher current; arc spot size affects heat concentration
Substrate Thermal Properties	k, ρ, Cp	Material-specific (SS, CS, Ni-alloy)	Lower k increases penetration; higher Cp reduces thermal gradient

4.2 Implementation Workflow

1. Step 1 — Material Property Definition: Compile temperature-dependent thermal conductivity, specific heat, and density for both the base material and the overlay filler metal. For common materials such as 304/316 stainless steel, 309L, 316L, Inconel 625, and carbon steel, these properties are well-documented in ASM and CRC handbooks.
2. Step 2 — Heat Source Model Selection: Select the appropriate heat source model. For variable-speed conditions, a modified double-ellipsoid (Goldak) model or a cone-cylinder hybrid model is recommended, with the heat source velocity set as a time-dependent function v(t).
3. Step 3 — Boundary and Initial Conditions: Define convective and radiative heat loss at the workpiece surfaces. For multi-pass overlay, the initial temperature field for pass n is the residual temperature field from pass n−1 after interpass cooling.
4. Step 4 — Numerical Solution: Solve the transient heat equation using finite element (FE) or finite difference (FD) methods. Commercial software such as ANSYS, DEFORM, or proprietary in-house codes can be employed.
5. Step 5 — Penetration Extraction: From the computed temperature field, extract the isotherm corresponding to the melting point of the base metal (e.g., 1395°C for 304 SS, 1425°C for 316 SS) to determine the penetration profile at each time step.
6. Step 6 — Validation Against Physical Trials: Compare model predictions with measured penetration from macrographically examined qualification welds. Adjust model parameters (e.g., heat source efficiency η, typically 0.6–0.8 for GTAW) until prediction accuracy is within ±10%.

4.3 Key Technical Considerations for Overlay Applications

• Dilution Control: In overlay welding, the goal is often to minimize base metal dilution to preserve the corrosion or wear properties of the overlay layer. The model enables prediction of dilution as: Dilution (%) = (Volume of melted base metal / Total weld volume) × 100%. Target dilution is typically <10% for austenitic stainless overlays on carbon steel and <5% for Ni-base overlays per NACE MR0175 requirements.
• Residual Stress Prediction: The temperature field model can be coupled with a thermal-stress analysis to predict residual stress distributions in the overlay, which is critical for applications subject to cyclic loading or where cracking resistance is required per ASME Section VIII Div. 1.
• Microstructure Prediction: The cooling rate derived from the temperature field (particularly the 800°C–500°C cooling interval, δt_800-500) correlates with weld metal grain size and phase composition. This is essential for predicting susceptibility to sensitization (σ-phase, carbide precipitation) in 300-series stainless overlays.

5. Applicable Standards and Acceptance Criteria

5.1 Governing Standards

The penetration prediction model and its outputs must align with the following standards and specifications:

• ASME Section IX: Governs qualification of welding procedures, welders, and welding operators. The model's output supports WPS development by providing predicted essential variables (heat input, travel speed, preheat) that must be qualified per QW-250 through QW-270.
• ASME Section VIII, Division 1: For pressure vessel overlay applications, weld geometry and penetration must meet the requirements of UG-100 through UG-116. The model ensures predicted penetration meets minimum requirements for full-penetration or partial-penetration welds as specified.
• ASME B31.3: For process piping overlay repairs, the model informs the design of overlay welds on piping per paragraph 341.3, ensuring adequate penetration and dilution control.
• ASTM A240: For stainless steel overlay materials (304, 316, 321, etc.), the model's thermal predictions must ensure that the weld metal microstructure remains compliant with the grade-specific requirements.
• NACE MR0175 / ISO 15156: For sour service applications, the model must predict dilution levels that ensure the overlay weld metal meets the hardness limit (≤ 22 HRC) and composition requirements for H₂S-resistant materials.
• GB/T 985.1-2008: Chinese national standard for butt weld preparation and penetration requirements, applicable when the model is used for GB-compliant qualification procedures.
• NB/T 47014-2011: Chinese pressure vessel welding procedure qualification standard. The model supports PQR development under this standard by predicting penetration and dilution for each trial weld.
• ISO 15614-1: International standard for qualification of welding procedures for metallic materials. The model's predictions of essential variables must fall within the qualified range of the PQR.
• ASTM E165: Standard practice for liquid penetrant inspection, used to verify that predicted penetration depths result in fusion boundaries that are free of cracks and incomplete fusion.
• GB/T 3323.1: Chinese standard for radiographic testing of welds, used to verify actual penetration against model predictions during qualification.

5.2 Acceptance Criteria for Model Validation

Acceptance Parameter	Target Accuracy	Verification Method
Penetration depth prediction	±10% of measured value	Macrographical examination of qualification coupons (GB/T 985.1, ASTM E20)
Dilution rate prediction	±3 percentage points	Optical emission spectrometry (OES) or XRF analysis of weld cross-sections
Heat input calculation	±5% of actual	Instrumented welding monitoring (current, voltage, speed logging)
Fusion boundary width	±15% of measured value	Macrographical examination and metallographic preparation
Cooling rate (δt800-500)	±20% of measured value	Thermocouple-instrumented trials or thermal simulation cross-check

6. Common Risks and Controls

6.1 Technical Risks

Risk	Consequence	Mitigation Control
Over-reliance on model predictions without physical validation	Unqualified WPS leading to weld rejection or equipment failure	Mandate physical PQR for every WPS; use model only for pre-screening and parameter optimization, not as a substitute for qualification testing
Inaccurate material property inputs (temperature-dependent k, Cp)	Systematic error in predicted penetration and dilution	Use peer-reviewed property databases (ASM, NIST); validate with thermocouple trials for critical applications
Failure to account for multi-pass thermal accumulation	Under-prediction of penetration in upper passes; excessive dilution in final overlay layers	Implement sequential pass-by-pass simulation with residual temperature carry-forward; validate with multi-pass macrographical trials
Variable-speed profile not representative of actual operator behavior	Model predictions diverge from actual weld geometry in production	Record actual travel speed profiles from production welds (via CNC logs or manual speed tracking); feed real profiles into the model
Neglecting latent heat of fusion in the thermal model	Over-prediction of penetration depth by 10–20%	Implement enthalpy method or equivalent latent heat treatment in the numerical solver

6.2 Quality and Compliance Risks

• WPS Deviation Risk: If production operators deviate from the qualified travel speed range, the penetration and dilution may fall outside the qualified envelope. Control: Implement real-time welding parameter monitoring with automated alarms for out-of-specification speed deviations, per ASME Section IX QW-301 requirements for procedure adherence.
• Documentation Gap: The model's assumptions, input data, and validation results must be documented for audit purposes. Control: Maintain a model validation dossier containing input property data, mesh convergence studies, physical trial results, and prediction-vs-actual comparison tables, aligned with ISO 9001:2015 Clause 8.5.1 (Controlled Production) and ASME NQA-1 requirements for nuclear applications.

7. Application Scenarios Across the Three Technology Routes

7.1 TIG/MIG Weld Overlay (Primary Application)

This is the core application domain. The penetration prediction model directly supports the following overlay operations:

• Corrosion-Resistant Overlay: Multi-pass overlay of 309L/316L/Inconel 625 on carbon steel substrates for chemical reactor internals, heat exchanger tubesheets, and pump casings. The model predicts dilution to ensure the final overlay maintains >90% austenitic or Ni-base composition, meeting NACE MR0175 and ASTM B625 requirements.
• Wear-Resistant Overlay: Single-pass or multi-pass overlay of Stellite 6, Hardox, or carbide-containing alloys on valve seats, pump impellers, and crusher components. The model optimizes travel speed to achieve target penetration (typically 1–3 mm) while maximizing overlay material deposition.
• Repair Overlay: Overlay welding on damaged or corroded components in service. The model accounts for variable travel speeds at repair boundaries where the welder transitions from straight sections to contour-following, predicting penetration variation to ensure complete fusion at transition zones.
• Transition Layer Welding: When overlaying dissimilar materials (e.g., Ni-base on carbon steel), a transition layer (e.g., 309L or 80%Ni/20%Fe) is required. The model predicts penetration into the substrate and dilution into the transition layer to ensure the correct metallurgical compatibility per ASME Section IX QW-250.

7.2 Hydraulic Explosive Bonding (Indirect Application)

• Post-Bonding Overlay Design: When hydraulic explosive bonding is used to create a clad plate (e.g., 316L on carbon steel), the bonded layer may be thinner than the required overlay thickness. Additional weld overlay passes may be applied on top of the bonded layer. The penetration prediction model ensures that these additional overlay passes do not penetrate through the bonded layer and damage the explosive bond interface.
• Edge Repair Welding: The edges of hydraulic explosive bonded plates often require weld repair. The model predicts penetration in these repair welds to ensure they do not undercut the bonded interface, maintaining bond integrity per ASTM A284 requirements.

7.3 Explosion Welding (Indirect Application)

• Clad Plate Post-Processing: Explosion-welded clad plates (e.g., Inconel 625 on 16Mn steel per GB/T 12770) may require additional weld overlay for thickness build-up or surface finishing. The penetration model guides the overlay process to avoid excessive heat input that could degrade the explosive bond quality (delamination, intermetallic compound formation).
• Weld Repair on Explosion-Welded Components: For explosion-welded pipes or plates that require local weld repair, the model predicts the thermal field to ensure the repair weld does not compromise the bond interface integrity, maintaining compliance with ASTM A284 and ASME PCC-2-2021.

8. Contribution to Qualification Building, Product Delivery, and Customer Value

8.1 Qualification Building

The penetration prediction model accelerates and strengthens the company's qualification portfolio:

• WPS Library Expansion: By pre-screening parameter combinations through modeling, the company can develop a broader library of qualified WPSs for different substrate-overlay-material combinations more efficiently. Each model-validated parameter set reduces the number of physical PQRs needed, saving material costs and laboratory time.
• Essential Variable Control: The model quantifies the sensitivity of penetration to each essential variable (travel speed, current, voltage, heat input), enabling precise definition of WPS essential variable ranges per ASME Section IX QW-250. This reduces the risk of WPS invalidation due to minor parameter drift.
• Multi-Pass Qualification: For multi-pass overlay WPSs, the model provides pass-by-pass penetration predictions, supporting the development of qualified multi-pass procedures that meet the requirements of NB/T 47014-2011 and ISO 15614-1 for multi-layer weld qualification.

8.2 Product Delivery

• Faster First-Article Approval: With model-predicted penetration and dilution data available before the first production weld, the company can submit more comprehensive technical packages to the customer's engineering team, accelerating first-article approval and reducing project schedule risk.
• Reduced Rework and Scrap: Accurate penetration prediction minimizes the risk of under-penetration (incomplete fusion, requiring rework) or over-penetration (excessive dilution, requiring overlay redo). This directly reduces production cost and delivery schedule risk.
• Scalable Process Transfer: When the same overlay specification must be applied across multiple production sites or shifts, the model provides a standardized, physics-based process definition that is independent of individual operator skill, ensuring consistent product quality.

8.3 Customer Value

• Engineering Transparency: Customers in high-integrity industries (nuclear, oil & gas, power generation) increasingly demand model-based process justification beyond empirical qualification. The company's ability to present a validated temperature field model with penetration predictions demonstrates engineering rigor and reduces customer qualification burden.
• Life-Cycle Cost Reduction: By optimizing overlay parameters to minimize dilution and control residual stress, the model contributes to longer service life of clad components, reducing the customer's long-term maintenance and replacement costs.
• Customized Solutions: For customers with non-standard overlay requirements (unusual geometries, variable travel speed profiles, exotic material combinations), the model enables rapid parameter optimization without extensive physical trial programs, reducing quotation-to-delivery cycle time.

9. Recommendations for Operational Integration

1. Establish a Model Validation Protocol: Formalize a validation procedure requiring at least three physical trial welds per material combination, with macrographical and spectroscopic verification of model predictions. Maintain a validation database for ongoing model refinement.
2. Integrate with CNC Welding Systems: Where automated GTAW/MIG systems are used, integrate the model's recommended travel speed profiles into the CNC program to ensure actual welding parameters match the model assumptions.
3. Develop Operator Training Modules: Create training materials that use the model's predictions to teach operators how travel speed affects weld geometry, with visualizations of temperature field and penetration profiles at different speeds.
4. Extend to MIG Overlay Applications: Adapt the temperature field model to include the GMAW (MIG) heat source, which has a different heat distribution profile due to the transfer mode (short-circuit, globular, spray). This expands the model's applicability to the company's full TIG/MIG overlay capability.
5. Pursue Peer-Reviewed Publication: Publish the model's methodology and validation results in relevant journals (e.g., Welding Journal, International Journal of Advanced Manufacturing Technology, 焊接学报) to establish the company's technical authority and attract high-value customers who value engineering depth.

10. Conclusion

The variable-speed GTAW temperature field analysis model and penetration prediction capability represents a significant intellectual asset for Cladding Technology Shanxi Co., Ltd. It transforms the company's TIG/MIG weld overlay operations from empirical practice to predictive engineering, directly supporting WPS qualification efficiency, product quality consistency, and customer confidence. While its primary application is in weld overlay, its analytical framework extends to post-bonding weld design in hydraulic explosive bonding and explosion welding applications. By systematically validating, documenting, and integrating this model into the company's quality management system, Cladding Technology Shanxi Co., Ltd. can position itself as a technically differentiated supplier in the competitive cladding and overlay market, meeting the increasingly demanding qualification and performance requirements of its customers across the oil & gas, power, chemical, and nuclear industries.