SAPSO-BP Neural Network Modeling for CO₂ Phase-Transformation Cracking Prediction and Sensitivity Analysis in Weld Overlay Cladding

1. Definition and Fundamental Principles

1.1 CO₂ Phase-Transformation Cracking: Mechanism and Context

Phase-transformation cracking (also termed transformation cracking or ductile-to-brittle transformation cracking) is a critical solidification and solid-state cracking mechanism that occurs during the cooling of weld metal deposits, particularly in weld overlay and cladding operations. In processes employing CO₂ or CO₂-rich mixed shielding gases—such as CO₂/MIG (GMAW) overlay welding—the elevated carbon activity introduced by the CO₂ shielding atmosphere promotes the formation of hard, brittle martensitic phases in the weld metal upon cooling. This rapid austenite-to-martensite transformation generates volumetric expansion that, when constrained by the surrounding cooler substrate and previously deposited layers, produces tensile stresses exceeding the fracture toughness of the newly formed martensite, resulting in microcracks and macrocracks within the weld overlay deposit.

The phenomenon is particularly severe in the following scenarios:

High-carbon steel substrates: where carbon diffusion from the base metal into the weld pool raises the effective carbon content beyond the cracking threshold.
Low-heat-input deposition: which accelerates cooling rates, promoting extensive martensite formation.
Multi-layer overlay without interpass temperature control: where each successive layer cools rapidly against the still-warm but rigid previous layer.
Cracking-sensitive alloy systems: including martensitic stainless steels (e.g., 410, 420), high-strength low-alloy steels, and certain nickel-based overlay alloys deposited on carbon steel substrates.

1.2 The Role of CO₂ in the Shielding Atmosphere

CO₂ shielding gas is widely used in MIG/MAG weld overlay due to its low cost, excellent arc stability, and good penetration characteristics. However, CO₂ dissociates at arc temperatures into atomic carbon and oxygen, both of which interact with the molten weld pool. The atomic carbon increases the carbon activity in the weld metal, while the oxygen contributes to oxide inclusions and embrittling phases. The combined effect is a weld metal composition that is significantly more prone to martensitic transformation and subsequent cracking than would be predicted by the nominal electrode composition alone. This "CO₂ effect" is a well-documented phenomenon in the welding literature and represents a persistent challenge in industrial cladding operations.

2. Technical Purpose and Value of SAPSO-BP Prediction Modeling

2.1 Why Traditional Approaches Are Insufficient

Conventional approaches to predicting phase-transformation cracking in weld overlay rely on:

Empirical carbon equivalent formulas: such as C_eq = C + Mn/6 + (Cr+Mo+V)/5 + (Ni+Cu)/15, which provide a first-order assessment but lack the precision required for process optimization.
Thermodynamic software (e.g., JMatPro, Thermo-Calc): which can predict phase fractions but require extensive calibration for each specific welding system and do not readily incorporate process parameter interactions.
Extensive coupon testing: which is costly, time-consuming, and limited to discrete parameter combinations, failing to capture the continuous, nonlinear relationships between multiple process variables and cracking susceptibility.

2.2 The SAPSO-BP Neural Network Approach

The SAPSO-BP methodology combines two complementary computational techniques to overcome these limitations:

SAPSO (Simulated Annealing–Particle Swarm Optimization): A hybrid metaheuristic optimization algorithm that integrates the global exploration capability of Particle Swarm Optimization (PSO) with the local refinement and escape-from-local-minima capability of Simulated Annealing (SA). In this application, SAPSO is employed to optimize the architecture, weights, and biases of the BP neural network, ensuring that the trained model achieves high prediction accuracy without overfitting.

BP Neural Network (Backpropagation Neural Network): A multi-layer feedforward neural network trained using the backpropagation algorithm to learn the complex, nonlinear mapping between welding process parameters (inputs) and phase-transformation cracking susceptibility (output). The network architecture typically includes an input layer (process parameters), one or more hidden layers (nonlinear feature extraction), and an output layer (cracking index or probability).

2.3 Sensitivity Analysis

The sensitivity analysis component systematically quantifies the relative influence of each input parameter on the predicted cracking outcome. This is achieved through methods such as:

Weight-based sensitivity: analyzing the magnitude of trained connection weights between input neurons and hidden neurons.
Partial derivative analysis: computing the rate of change of the output with respect to each input parameter across the operating range.
Simulation-based sensitivity: varying each parameter individually while holding others constant and observing the output response magnitude.

The sensitivity analysis results directly inform process development priorities, WPS design decisions, and quality control focus areas.

3. Key Process Parameters and Modeling Framework

3.1 Input Parameters for the Prediction Model

The SAPSO-BP model incorporates a comprehensive set of welding and metallurgical parameters as inputs. The following table summarizes the primary parameter categories and their typical ranges in weld overlay cladding applications:

Parameter Category	Specific Parameter	Typical Range (Weld Overlay)	Influence on CO₂ Phase-Transformation Cracking
Thermal Input	Welding current (I)	150–400 A (MIG/MAG)	Higher current increases heat input, reduces cooling rate, decreases martensite fraction
Thermal Input	Travel speed (v)	200–800 mm/min	Faster speed increases cooling rate, increases martensite, increases cracking risk
Thermal Input	Heat input (q)	0.5–5.0 kJ/mm	Primary thermal control parameter; low q strongly promotes cracking
Thermal Input	Interpass temperature (T_ip)	50–250 °C	Higher T_ip reduces cooling rate of subsequent layers, reduces cracking
Shielding Atmosphere	CO₂ fraction in shielding gas	0–100% CO₂	Higher CO₂ increases carbon activity, promotes martensite, increases cracking
Shielding Atmosphere	Shielding gas flow rate	8–25 L/min	Inadequate flow allows atmospheric contamination; excess flow causes turbulence
Electrode/Wire	Electrode composition (C, Mn, Cr, Ni, Mo, etc.)	Alloy-specific	Higher base alloy carbon content increases cracking susceptibility
Electrode/Wire	Wire diameter (d)	0.8–1.6 mm	Affects heat input per pass and dilution rate
Substrate	Base metal carbon equivalent	0.2–0.8% C_eq	Higher C_eq of substrate increases dilution-related carbon in weld
Substrate	Preheat temperature (T_p)	50–250 °C	Higher preheat reduces initial cooling rate, reduces cracking
Geometry	Number of overlay layers	1–10+ layers	More layers increase cumulative restraint and thermal cycling
Geometry	Overlay thickness per pass	1–5 mm	Affects thermal mass and cooling rate

3.2 Output Parameters and Cracking Assessment

The model output typically represents one or more of the following:

Cracking susceptibility index: a normalized score (0–1) indicating the probability or severity of phase-transformation cracking.
Predicted martensite fraction: the estimated volume fraction of martensite in the weld metal upon cooling to room temperature.
Maximum residual tensile stress: the predicted peak tensile stress developed during martensitic transformation.
Crack length or crack density: for models trained on experimental data including crack characterization.

3.3 Model Architecture and Training

The SAPSO-BP model is typically structured as follows:

Input layer: 10–15 neurons corresponding to the process parameters listed above.
Hidden layer(s): 1–2 hidden layers with 20–60 neurons each, using sigmoid or ReLU activation functions to capture nonlinear parameter interactions.
Output layer: 1–3 neurons corresponding to the cracking assessment outputs.
Training dataset: 100–500 experimental or simulation data points obtained from coupon weld overlay tests under systematically varied conditions.
Optimization: SAPSO optimizes the initial weights and biases of the network before BP training commences, with SA providing perturbation to escape local minima during the optimization process.

4. Sensitivity Analysis Results and Process Development Implications

4.1 Typical Sensitivity Ranking

Based on the literature and typical SAPSO-BP modeling results for CO₂ phase-transformation cracking in weld overlay, the sensitivity ranking of process parameters generally follows this order (from most to least influential):

Heat input (q) / Welding current (I) and travel speed (v): The thermal input is consistently the most influential parameter. Low heat input directly increases cooling rate, which is the primary driver of martensite formation and subsequent transformation cracking. The sensitivity analysis typically shows that reducing heat input below a critical threshold causes a nonlinear (exponential-like) increase in cracking susceptibility.
Interpass temperature (T_ip): The second most influential parameter in multi-layer overlay. Maintaining adequate interpass temperature is critical for reducing cracking in subsequent layers, as it effectively reduces the cooling rate experienced by each new deposit.
CO₂ fraction in shielding gas: Directly controls the carbon activity increment in the weld pool. Moving from Ar/CO₂ mixed gas (e.g., 80/20 Ar/CO₂) to pure CO₂ can significantly increase cracking susceptibility.
Electrode composition (carbon content): The nominal carbon content of the filler metal, combined with dilution from the base metal, determines the effective carbon content of the weld metal and thus its transformation behavior.
Preheat temperature (T_p): Influences the initial cooling rate of the first layer and sets the baseline thermal conditions for subsequent layers.
Base metal carbon equivalent: Affects dilution-related carbon pickup in the weld metal, particularly in the first layer.
Wire diameter and overlay geometry: Secondary parameters that influence heat input distribution and thermal mass effects.

4.2 Process Window Identification

The sensitivity analysis enables the identification of critical process windows—combinations of parameters within which cracking susceptibility remains below a defined threshold. These process windows are directly transferable to WPS development and production parameter settings.

5. Applicable Standards and Acceptance Criteria

5.1 Welding Procedure Qualification Standards

The SAPSO-BP prediction model serves as a supporting tool for welding procedure qualification under the following standards:

ASME Section IX: The model can be used to establish the essential variables and their acceptable ranges for weld overlay qualification, particularly for variables related to heat input, preheat, and interpass temperature. The prediction results can supplement the mandatory weld coupon testing required by QW-200 through QW-400.
NB/T 47014 (Chinese National Boiler Standard): For pressure vessel weld overlay qualification in China, the model provides a predictive basis for establishing the procedure's essential variables and their qualification ranges.
GB/T 19866 (Chinese National Standard for Welding Procedure Specification): The sensitivity analysis results inform the classification of essential variables and their permissible variations for procedure qualification.
ISO 15614-1: The model supports the qualification of welding procedures for weld overlay applications under this international standard.
API 16C / API 16F: For pipeline cladding and repair applications, the model assists in establishing qualified welding procedures for overlay cladding of corrosion-resistant alloys on carbon steel pipe.
NACE MR0175 / ISO 15156: For sour service applications, the model ensures that overlay deposits meet the hardness and cracking resistance requirements specified for H₂S-containing environments.

5.2 Acceptance Criteria for Overlay Deposits

The following acceptance criteria apply to weld overlay deposits where phase-transformation cracking is a concern:

Visual inspection (VT): No surface cracks, porosity exceeding acceptance limits per ASME Section IX or applicable product standard.
Penetrant testing (PT): No linear indications exceeding the acceptance criteria per ASTM E165 or equivalent.
Ultrasonic testing (UT): No indications of cracking or lack of fusion exceeding the acceptance criteria per ASME Section V Article 4 or ASTM E164.
Magnetic particle testing (MT): No indications of surface or near-surface cracks per ASTM E709.
Hardness testing: Maximum hardness of the overlay deposit must comply with the applicable product standard (e.g., ≤ 22 HRC for NACE MR0175 sour service).
Macrograph examination: No visible cracking in the weld metal or heat-affected zone upon metallographic examination per ASTM E3.
Chemical analysis: Weld metal composition within the specified range, with particular attention to carbon content.

5.3 Relevant Standards for CO₂ Shielding Gas and Weld Overlay

Standard	Title / Scope	Relevance to CO₂ Phase-Transformation Cracking
ASME Section IX	Welding, Brazing, and Fusing Qualifications	Procedure qualification requirements for weld overlay
ASTM A240	Stainless Steel Plate and Sheet	Substrate and overlay material specifications
AWS A5.9 / A5.18	Stainless Steel Welding Electrodes / Wire	Filler metal specifications for overlay welding
GB/T 8110	Welding Consumables - Welding Wires	Chinese standard for welding wire specifications
GB/T 14993	Welding Consumables - Gas Shielding	Chinese standard for shielding gas specifications
NB/T 47014	Qualification Test for Welding Procedures	Chinese standard for pressure vessel welding procedure qualification
ASME B31.3	Piping Code - Process Piping	Overlay cladding requirements for process piping
API 16C	Field Repair of Oil and Gas Pipelines	Overlay repair and cladding of pipelines
ISO 15156	Sour Service Materials	Hardness and cracking resistance requirements for H₂S service

6. Application Across the Three Technology Routes

6.1 TIG/MIG Weld Overlay (GMAW/GTAW Overlay)

The SAPSO-BP model is most directly applicable to the TIG/MIG weld overlay route, where CO₂ shielding gas is commonly employed. The model's primary value in this route includes:

WPS optimization: Identifying the minimum heat input threshold below which cracking becomes unacceptable, enabling the establishment of qualified parameter windows with confidence.
Shielding gas selection: Quantifying the cracking penalty of pure CO₂ versus mixed Ar/CO₂ shielding, supporting cost-benefit decisions for gas selection.
Multi-layer strategy development: Optimizing interpass temperature and layer sequence to minimize cracking in thick overlay deposits.
Transition layer design: Predicting the cracking susceptibility of transition layers (e.g., 309L deposited on carbon steel before a 316L overlay) under CO₂ shielding conditions.
High-strength steel overlay: Assessing the cracking risk when overlaying stainless or nickel alloys on high-carbon or high-strength steels.

Specific process recommendations derived from SAPSO-BP sensitivity analysis:

Scenario	Recommended Heat Input	Shielding Gas	Interpass Temperature	Preheat	Notes
309L/316L overlay on low-carbon steel (C ≤ 0.2%)	1.0–3.0 kJ/mm	80/20 Ar/CO₂	≥ 100 °C	≥ 50 °C	Low cracking risk; standard practice
309L/316L overlay on medium-carbon steel (C 0.2–0.4%)	2.0–4.0 kJ/mm	90/10 Ar/CO₂ or pure Ar	≥ 150 °C	≥ 100 °C	Moderate cracking risk; heat input critical
309L/316L overlay on high-carbon steel (C > 0.4%)	3.0–5.0 kJ/mm	Pure Ar or He/Ar	≥ 200 °C	≥ 150 °C	High cracking risk; CO₂ not recommended
Martensitic stainless (410/420) overlay on carbon steel	2.5–5.0 kJ/mm	Pure Ar	≥ 200 °C	≥ 200 °C	Very high cracking risk; post-weld heat treatment required

6.2 Hydraulic Explosive Bonding (HEB)

While hydraulic explosive bonding does not involve melting or CO₂ shielding gas, the SAPSO-BP model's underlying metallurgical understanding and sensitivity analysis methodology have indirect but valuable applications:

Post-bonding weld overlay: Hydraulic explosive bonded clad plates often require additional weld overlay layers to build up thickness or to repair bonding defects. The SAPSO-BP model directly applies to these overlay operations, ensuring that the bonding interface is not damaged by cracking in the overlay weld.
Thermal management of bonded assemblies: Understanding the thermal behavior of clad assemblies (predicted through similar neural network approaches) informs the design of subsequent welding operations on bonded products.
Material selection for bonded systems: The sensitivity analysis framework can be extended to evaluate how substrate composition affects the feasibility of subsequent weld overlay on HEB products, supporting material selection for bonded clad plate design.

6.3 Explosion Welding (EW)

Similar to HEB, explosion welding produces solid-state bonds without melting, so CO₂ phase-transformation cracking does not occur during the bonding process itself. However, the SAPSO-BP model contributes in the following ways:

Overlay weld repair of EW bonds: When explosion-welded clad plates require local repair or additional overlay layers, the SAPSO-BP model ensures that the repair welding procedure is qualified against phase-transformation cracking, preserving the integrity of the explosion weld bond.
WPS development for post-EW operations: Explosion-welded products often undergo machining, welding, or heat treatment. The model supports the development of qualified welding procedures for any subsequent weld operations on these products.
Hybrid process design: In hybrid manufacturing routes combining explosion welding with weld overlay (e.g., EW bonding followed by MIG overlay to achieve required thickness), the SAPSO-BP model ensures the overlay portion is optimized against cracking while maintaining compatibility with the explosion-welded interface.

7. Common Risks and Controls

7.1 Technical Risks

Risk	Description	Control Measures
Model overfitting	BP neural network trained on limited data may not generalize to new parameter combinations	Use SAPSO for weight initialization; employ cross-validation; maintain minimum 200 training data points; validate with independent test set
Inadequate training data	Insufficient experimental data leads to unreliable predictions	Systematically vary all input parameters across their full ranges; supplement with finite element simulation data; use transfer learning from related welding systems
Unmodeled parameters	Important parameters (e.g., surface contamination, ambient conditions) may be omitted	Conduct sensitivity analysis to identify missing parameters; include environmental factors as inputs; validate model against production welds
Cracking misclassification	Confusing phase-transformation cracking with hydrogen cracking or hot cracking	Use metallographic examination (ASTM E3) and fractography to classify crack type; ensure training data is properly labeled; include crack morphology features as inputs
Shielding gas contamination	CO₂ gas purity and flow rate variability affect actual carbon pickup	Monitor gas purity (≥ 99.5% CO₂ or specified mixture); use flow meters with alarms; include gas purity as model input

7.2 Quality Control Risks

Risk	Description	Control Measures
Unqualified WPS	WPS developed without considering CO₂ cracking effects may fail in production	Use SAPSO-BP model to pre-screen WPS parameter combinations; require model validation before WPS qualification testing; maintain model as a living document
Production parameter drift	Actual production parameters deviate from qualified WPS ranges	Implement real-time monitoring of heat input, interpass temperature, and gas flow; use model to define alarm thresholds; integrate with MES/QMS systems
Non-conforming overlay deposits	Cracking detected in production overlay welds	Implement 100% PT/MT inspection for cracking-sensitive overlays; perform hardness testing per NACE MR0175; conduct macrograph examination on witness coupons

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

8.1 Qualification Building

Accelerated WPS qualification: The SAPSO-BP model reduces the number of trial WPS variations required for qualification testing by pre-identifying viable parameter windows, potentially reducing qualification cycle time by 40–60%.
Essential variable definition: Sensitivity analysis results provide quantitative evidence for classifying variables as essential, supplementary, or non-essential under ASME Section IX or NB/T 47014, strengthening the technical basis for WPS qualification.
Cross-qualification support: The model supports the demonstration of procedure coverage across different substrate materials, filler metals, and process conditions, enabling efficient cross-qualification of welding procedures.
Customer qualification packages: Provides a comprehensive technical dossier demonstrating that the WPS was developed using state-of-the-art predictive modeling, enhancing customer confidence in the qualification.

8.2 Product Delivery

Reduced rework and scrap: By predicting and preventing phase-transformation cracking, the model directly reduces weld rework rates, improving on-time delivery and reducing cost of quality.
Process consistency: The model enables the establishment of precise parameter control limits, ensuring consistent overlay quality across production shifts, operators, and equipment.
Scalability: The model can be rapidly adapted to new substrate-filler combinations and new product geometries, accelerating the ramp-up of new product lines.
Traceability: Model predictions can be integrated into the product traceability system, providing a documented basis for each overlay weld's qualification status.

8.3 Customer Value

Risk reduction: Customers receive overlay cladding products with demonstrably lower cracking risk, reducing in-service failure probability and extending equipment life.
Technical transparency: The model provides customers with a transparent, data-driven explanation of why specific process parameters were selected, supporting informed decision-making.
Compliance assurance: The model supports compliance with stringent industry standards (ASME, API, NACE, NB/T) by quantitatively demonstrating that cracking susceptibility is within acceptable limits.
Cost optimization: By identifying the minimum acceptable heat input and the maximum permissible CO₂ fraction, the model enables customers to reduce shielding gas costs (using more CO₂ where safe) and improve welding productivity (using lower heat input where safe).
Competitive differentiation: The use of AI-driven predictive modeling positions the company as a technologically advanced cladding service provider, differentiating from competitors relying solely on empirical approaches.

9. Implementation Roadmap

Phase 1 – Data Collection: Conduct systematic coupon welding tests varying all input parameters across their operational ranges. Perform metallographic examination, hardness testing, and crack characterization on each coupon. Target: 200–500 qualified data points.
Phase 2 – Model Development: Build the BP neural network architecture; use SAPSO to optimize initial weights and biases; train the model on the collected dataset; validate with an independent test set (target: prediction accuracy ≥ 90% for cracking/non-cracking classification).
Phase 3 – Sensitivity Analysis: Perform comprehensive sensitivity analysis to rank parameter influences; identify critical process windows; develop process control guidelines.
Phase 4 – WPS Integration: Integrate model predictions into the WPS development workflow; use the model to pre-screen WPS variations before qualification testing; document model usage in WPS technical dossiers.
Phase 5 – Production Deployment: Deploy the model as a decision support tool for production planning; integrate with real-time monitoring systems; establish model update protocols based on production feedback.
Phase 6 – Continuous Improvement: Regularly update the model with new production data; expand the model to cover additional welding systems and material combinations; explore extension to other cracking mechanisms (hydrogen cracking, hot cracking, solidification cracking).

10. Conclusion

The SAPSO-BP neural network approach to CO₂ phase-transformation cracking prediction and sensitivity analysis represents a significant advancement in the intelligent optimization of weld overlay cladding processes. By replacing empirical guesswork with data-driven prediction, this methodology directly addresses the persistent challenge of cracking in CO₂-shielded MIG/MAG weld overlay operations. The sensitivity analysis component provides actionable insights for process development, WPS qualification, and production quality control. When integrated into the company's three technology routes—TIG/MIG weld overlay, hydraulic explosive bonding, and explosion welding—the model ensures that all overlay welding operations, whether primary or post-bonding repair, are optimized against phase-transformation cracking. This contributes directly to qualification efficiency, product reliability, regulatory compliance, and ultimately, customer value through reduced in-service failure risk and extended equipment life.