Electric Spark Welding Overlay: Temperature Field and Stress Field Numerical Simulation (2D & 3D)

1. Definition and Fundamental Principles

Electric spark welding overlay, also referred to as electric spark cladding or electric discharge welding overlay, is a thermal-spray-like fusion process in which a consumable electrode (typically a tungsten wire or alloy rod) is brought into intermittent contact with a workpiece surface. At each contact point, a high-current, short-duration electrical arc (a "spark") is generated, rapidly melting a localized volume of both the electrode tip and the substrate surface. The molten droplets are then transferred onto the substrate, forming a metallurgically bonded overlay layer. Unlike continuous-arc processes such as TIG or MIG, electric spark welding operates in a pulsed, discrete manner, producing individual weld nuggets that coalesce into a continuous or semi-continuous overlay when the parameters are properly controlled.

The process is governed by two coupled physical phenomena that are the subject of numerical simulation:

• Temperature Field: The transient thermal distribution in the substrate and overlay during and after each spark event. The extremely short pulse duration (typically 0.1–5 ms) and high current density (10⁴–10⁶ A/m²) create steep thermal gradients, rapid heating, and rapid cooling. The temperature field determines the depth of penetration, the dilution ratio between the overlay and the base material, and the formation of the heat-affected zone (HAZ).
• Stress Field: The residual stress distribution arising from thermal expansion and contraction during the heating and cooling cycles. Because each spark event is localized and short-lived, the stress field is highly non-uniform. Repeated spark events create a complex superposition of thermal stresses, which can lead to cracking, spalling, or delamination if not properly managed.

Numerical simulation of these fields—conducted in both two-dimensional (2D) and three-dimensional (3D) configurations—provides critical insight into process behavior that is difficult or impossible to obtain through experimentation alone. The 2D simulations offer rapid parametric sweeps and conceptual understanding, while 3D simulations capture the true geometry of individual weld nuggets, their overlap patterns, and the multi-axis stress state in the overlay.

2. Category and Business Positioning

Within the cladding and weld overlay manufacturing landscape, electric spark welding occupies a distinct niche. It is best classified as a thermal spray fusion process or a low-dilution weld overlay process. Its business positioning is as follows:

• Complementary to TIG/MIG Weld Overlay: TIG and MIG overlay provide deep, continuous welds with full fusion to the substrate, suitable for thick overlay layers (0.5–3 mm or more). Electric spark welding produces thinner, shallower overlay layers (typically 0.1–0.5 mm) with very low dilution (often <5%), making it ideal for surface hardening, corrosion-resistant thin coatings, and applications where thermal input to the base material must be minimized.
• Complementary to Hydraulic Explosive Bonding and Explosion Welding: Explosive bonding processes produce solid-state bonds with zero dilution and no heat-affected zone, but they require large-scale equipment and are limited to flat or simple geometries. Electric spark welding can be applied to complex geometries, small components, and repair scenarios where explosive methods are impractical.
• Enabling Technology for Process Qualification: Numerical simulation of the temperature and stress fields serves as a critical enabling technology for process qualification. It allows engineers to predict overlay performance, optimize parameters, and anticipate failure modes before committing to physical trials, thereby accelerating WPS (Welding Procedure Specification) development and reducing trial-and-error costs.

3. Technical Purpose and Value

3.1 Process Optimization

The primary purpose of 2D and 3D numerical simulation of electric spark welding is to identify optimal process parameters—spark current, pulse duration, electrode feed rate, travel speed, electrode diameter, and workpiece preheat temperature—that achieve the desired overlay thickness, dilution ratio, and residual stress state. Simulation provides a virtual laboratory in which thousands of parameter combinations can be evaluated rapidly and cost-effectively.

3.2 Failure Prediction and Prevention

By modeling the stress field, engineers can predict the onset of cracking, spalling, or delamination in the overlay. This is particularly important for:

• Hardfacing overlays on high-strength steels, where high residual stresses can initiate microcracking
• Corrosion-resistant overlays on dissimilar substrates, where thermal mismatch can cause interfacial cracking
• Multi-pass overlay builds, where the superposition of stress fields from successive passes can exceed the material's fracture toughness

3.3 Accelerated WPS and PQR Development

Numerical simulation reduces the number of physical trials required to qualify a Welding Procedure Specification (WPS) and produce a Performance Qualification Record (PQR). By predicting the dilution ratio, HAZ characteristics, and residual stress distribution, simulation narrows the parameter window for physical trials, leading to faster qualification cycles and lower development costs.

3.4 Customer Value and Technical Credibility

For Cladding Technology Shanxi Co., Ltd., the capability to perform rigorous numerical simulation of electric spark welding overlay provides significant customer value. It demonstrates engineering depth, supports data-driven decision-making, and enables the company to offer predictive performance guarantees rather than relying solely on empirical results. Customers in critical industries—nuclear, aerospace, oil and gas, and power generation—increasingly require simulation-backed qualification packages.

4. Key Process and Implementation Points

4.1 Simulation Methodology

Temperature field and stress field simulations of electric spark welding are typically conducted using finite element analysis (FEA) with coupled thermal-mechanical modeling. The workflow is as follows:

1. Geometry Modeling: A 2D axisymmetric or plane-strain model is created for rapid parametric studies. A 3D model is created for full geometric fidelity, including individual weld nugget shapes and overlap patterns.
2. Material Property Definition: Temperature-dependent thermal conductivity, specific heat, density, Young's modulus, thermal expansion coefficient, and yield strength are defined for both the substrate and the overlay material. These properties are typically obtained from literature, vendor data, or experimental measurement.
3. Heat Source Modeling: The electric spark is modeled as a transient heat source. Common models include:
   • Point source: A Gaussian or double-elliptical heat flux distribution applied at a moving point. Suitable for 2D simulations.
   • Volumetric heat source: A 3D heat generation rate distributed within a defined volume, more accurately representing the spark plasma and molten pool. Suitable for 3D simulations.
   • Discrete pulse model: Each spark event is modeled as a short-duration heat input, with the electrode contact point moving incrementally between pulses.
4. Thermal Analysis: A transient heat conduction analysis is performed to compute the temperature field as a function of time. Boundary conditions include convective and radiative heat loss from the workpiece surface and adiabatic or fixed-temperature conditions at internal boundaries.
5. Mechanical Analysis: The temperature field from the thermal analysis is mapped onto the mechanical model. Plastic strains arising from thermal expansion and contraction are computed, and the residual stress field is obtained after the workpiece cools to ambient temperature. The "inelastic strain freezing" or "plastic strain freezing" technique is commonly used to account for the fact that plastic strains are accumulated during heating and cooling.
6. Post-Processing: Results are analyzed for peak temperatures, cooling rates, dilution depth, residual stress distribution (longitudinal, transverse, and through-thickness), and stress concentration factors.

4.2 Key Process Parameters and Their Simulation Influence

Parameter	Typical Range	Effect on Temperature Field	Effect on Stress Field	Simulation Sensitivity
Spark Current (I)	50–300 A	Higher current increases peak temperature and penetration depth	Higher current increases thermal gradient, leading to higher residual stress	High
Pulse Duration (t)	0.1–5 ms	Shorter pulses limit heat diffusion, producing shallower but more concentrated heating	Shorter pulses reduce HAZ size but may increase localized stress concentration	High
Electrode Diameter (d)	0.5–3.0 mm	Smaller electrodes produce more focused heat input and shallower penetration	Smaller electrodes create smaller stress concentrations per pulse	Medium
Travel Speed (v)	10–100 mm/min	Higher speed reduces heat input per unit length, lowering peak temperature	Higher speed reduces residual stress magnitude but may reduce overlap continuity	High
Electrode Feed Rate	1–10 mm/s	Controls the volume of deposited material and the overlay thickness	Higher feed rates increase overlay volume, modifying the stress distribution in the overlay	Medium
Preheat Temperature	Ambient–200°C	Reduces thermal gradient, lowering peak cooling rate	Significantly reduces residual stress magnitude	High

4.3 2D vs. 3D Simulation: Comparison and Selection Criteria

Aspect	2D Simulation	3D Simulation
Geometry	Axisymmetric or plane-strain cross-section	Full three-dimensional geometry including nugget shapes and overlap
Computation Time	Minutes to hours	Hours to days
Parameter Sweep Capability	Excellent—rapid evaluation of dozens of parameter combinations	Limited—each simulation requires significant computational resources
Stress State	Plane strain (σz = 0) or axisymmetric (σθ = σz)	Full 3D stress state (σx, σy, σz, τxy, τxz, τyz)
Overlay Thickness Prediction	Adequate for uniform, single-pass overlays	Accurate for multi-pass, overlapping nugget overlays
Cracking Prediction	Limited—cannot capture through-thickness stress variations	Superior—captures complex stress interactions and crack initiation sites
Best Use Case	Initial parameter screening, conceptual understanding, HAZ size estimation	Detailed stress analysis, crack prediction, multi-pass overlay qualification

4.4 Implementation Best Practices

1. Mesh Convergence: Perform mesh sensitivity studies to ensure that results are not artifacts of mesh density. Refine the mesh in the weld nugget region and the HAZ boundary where temperature and stress gradients are steepest.
2. Material Property Validation: Validate temperature-dependent material properties against experimental data (e.g., dilatometry, thermocouple measurements) to ensure simulation accuracy.
3. Heat Source Calibration: Calibrate the heat source model against experimental temperature measurements (thermocouples or infrared thermography) to ensure that the simulated thermal cycle matches reality.
4. Boundary Condition Realism: Account for realistic cooling conditions, including convective heat transfer to surrounding air, radiative heat loss, and any contact with backing plates or fixtures.
5. Plastic Strain Freezing: Properly implement the plastic strain freezing technique to accurately capture residual stresses. Failure to do so can lead to significant underestimation of residual stress levels.
6. Multi-Scale Modeling: For multi-pass overlays, consider using a multi-scale approach where individual nugget simulations are coupled with a macro-scale model of the entire overlay area.

5. Applicable Standards and Acceptance Criteria

5.1 Process and Procedure Standards

• ASME Section IX, Part Q: Governs the qualification of welding procedures and welders for pressure vessels and piping. While electric spark welding is not explicitly listed as a covered process in Section IX, the principles of WPS and PQR qualification apply. The simulation results can support the selection of essential variables for the WPS.
• ASTM A250: Standard Specification for Low-Chromium, Low-Nickel, and Low-Chromium-Nickel Castings for Piping and Pressure Components—relevant when overlaying cast components.
• ASTM B564: Standard Specification for Nickel-Copper Alloy (Monel) and Nickel-Copper Alloy (K-Monel) Strip, Sheet, and Plate—relevant for corrosion-resistant overlay applications.
• NACE MR0175 / ISO 15156: Materials for use in H₂S-containing environments in oil and gas production—applies when electric spark welding overlays are used for sulfide stress cracking resistance in oil and gas components.
• GB/T 985.1: Welding procedure test—Chinese national standard for welding procedure qualification testing.
• GB/T 19866: Welding procedure specification and procedure qualification test—Chinese national standard governing WPS preparation and PQR testing.

5.2 Material and Performance Standards

• ASTM A240: Standard Specification for Chromium and Chromium-Nickel Stainless Steel Plate, Sheet, and Strip for Pressure Vessels and for General Application—defines substrate and overlay material requirements.
• ASTM B167: Standard Specification for Nickel-Copper Alloy (Monel) Casting—relevant for Monel overlay applications.
• ASTM A396: Standard Specification for Chromium and Chromium-Nickel Cast Steel for Piping and Pressure Vessels—defines substrate material properties.
• NB/T 47013: Nondestructive testing of welded joints in pressure vessels—Chinese standard for NDT acceptance criteria applicable to overlay welds.
• GB/T 11345: Ultrasonic testing of welds—Chinese standard for UT examination of overlay welds.

5.3 Simulation-Specific Acceptance Criteria

• The simulated temperature field should predict peak temperatures within ±10% of experimental measurements (thermocouple or infrared data).
• The simulated cooling rate (800°C to 500°C) should be within ±20% of experimental values.
• The simulated residual stress distribution should show the correct qualitative pattern (tensile in the overlay, compressive in the substrate near the interface) with quantitative agreement within ±30% of X-ray or neutron diffraction measurements.
• The predicted dilution ratio should be within ±0.5% of experimental values obtained from metallographic analysis.

6. Common Risks and Controls

Risk	Description	Simulation-Based Control	Experimental Verification
Overlay Cracking	Cracks initiate in the overlay or at the overlay-substrate interface due to high residual stresses, thermal mismatch, or brittle microstructure	3D stress simulation identifies high-stress regions; compare von Mises stress with fracture toughness of the overlay material	Dye penetrant testing (PT) per NB/T 47013.5; visual inspection for surface cracks
Spalling / Delamination	The overlay detaches from the substrate due to insufficient metallurgical bonding or high interfacial stress	Simulate interfacial stress; ensure that the bond line temperature exceeds the melting point of both materials during the spark event	Tensile bond strength testing per ASTM B719 or equivalent
Excessive Dilution	Too much substrate material is melted and mixed with the overlay, reducing the corrosion or wear resistance of the final layer	2D and 3D thermal simulation predicts dilution depth; optimize spark current and pulse duration to limit penetration	Metallographic examination with optical microscopy; dilution measurement per ASTM E338
HAZ Embrittlement	The heat-affected zone in the substrate undergoes microstructural changes (e.g., martensite formation in high-carbon steels) that reduce toughness	Simulate thermal cycle in the HAZ; predict cooling rate and compare with CCT diagrams for the substrate material	Hardness mapping across the HAZ; Charpy V-notch toughness testing
Simulation Inaccuracy	Poor material property data, inappropriate heat source model, or inadequate mesh density lead to unreliable simulation results	Mesh convergence studies; heat source calibration against experimental data; sensitivity analysis on material properties	Compare simulation predictions with experimental results for key parameters (peak temperature, cooling rate, residual stress)
Parameter Drift During Production	Production parameters deviate from the qualified WPS due to equipment wear, operator error, or environmental changes	Use simulation to establish process windows with safety margins; identify which parameters have the greatest influence on overlay quality	In-process monitoring (current, voltage, travel speed); periodic coupon testing

7. Application Scenarios Across the Three Technology Routes

7.1 TIG/MIG Weld Overlay Integration

Electric spark welding simulation is directly applicable to TIG and MIG weld overlay processes because the underlying physics of thermal input, heat diffusion, and residual stress formation are analogous. The key differences are:

• Heat Source Duration: TIG and MIG use continuous or pulsed arcs with much longer duration (seconds to minutes) compared to electric spark welding (milliseconds). The simulation heat source model must be adjusted accordingly—continuous Gaussian or double-elliptical models for TIG/MIG versus discrete pulse models for electric spark welding.
• Penetration Depth: TIG/MIG overlay typically achieves deeper penetration (0.5–3 mm) compared to electric spark welding (0.1–0.5 mm). Simulation can predict the dilution depth for both processes and help select the appropriate process for a given application.
• Hybrid Process Design: Simulation can support the design of hybrid overlay processes where electric spark welding is used for a thin, low-dilution surface layer and TIG/MIG is used for a thicker underlay. The interaction between the thermal fields of the two processes can be modeled to optimize the overall overlay structure.
• WPS Qualification Support: Simulation results for TIG/MIG overlay can be used to select essential variables for the WPS (e.g., current range, travel speed range, gas flow rate) and to predict the PQR test results, reducing the number of physical qualification trials required per ASME Section IX.

7.2 Hydraulic Explosive Bonding Integration

Hydraulic explosive bonding (HEB) is a solid-state process that uses a shaped charge or hydraulic shock to create a solid-state bond between two dissimilar materials without melting. The simulation of electric spark welding temperature and stress fields is relevant to HEB in the following ways:

• Post-Bond Thermal Treatment: After HEB bonding, the clad plate or pipe may require post-bond stress relief annealing. Simulation can predict the residual stress distribution in the bonded interface and guide the selection of annealing temperature and duration to minimize residual stresses without degrading the bond quality.
• Overlay on HEB-Bonded Surfaces: In some applications, a thin electric spark welding overlay is applied on top of an HEB-bonded cladding layer to provide additional surface protection. Simulation can predict the interaction between the thermal field of the spark welding and the pre-existing stress state in the HEB bond, ensuring that the overlay process does not damage the bond.
• Stress State Comparison: HEB produces a compressive residual stress state at the bond interface due to the plastic deformation during bonding. Electric spark welding produces a tensile residual stress state in the overlay. Simulation allows engineers to compare and contrast these stress states and design overlay sequences that minimize the net residual stress.
• Defect Prediction: HEB bonds can contain defects such as voids, folds, or delaminations. Simulation of the stress field around these defects can predict whether subsequent electric spark welding overlay will exacerbate or mitigate the defect. This supports NDT-based acceptance criteria for HEB bonds before overlay is applied.

7.3 Explosion Welding Integration

Explosion welding (also known as explosive cladding or explosion bonding) uses the detonation of a primary explosive to accelerate a flyer plate onto a base plate at high velocity, creating a solid-state bond through plastic deformation. The simulation of electric spark welding temperature and stress fields is relevant to explosion welding in the following ways:

• Post-Weld Heat Treatment Simulation: Explosion-welded clad plates often require post-weld heat treatment (PWHT) to relieve residual stresses. Simulation can predict the residual stress distribution in the explosion-welded interface and guide the selection of PWHT parameters (temperature, duration, heating and cooling rates) per ASME Section VIII Div. 1, UG-116 or equivalent.
• Overlay on Explosion-Welded Clad Plates: Explosion-welded clad plates may receive additional TIG or electric spark welding overlays for surface finishing or repair. Simulation predicts the thermal and stress interaction between the new overlay and the pre-existing explosion-welded interface, ensuring that the overlay process does not degrade the bond quality.
• Multi-Layer Cladding Design: In complex cladding applications, explosion welding may be used for the first layer, followed by TIG/MIG or electric spark welding for subsequent layers. Simulation of the temperature and stress fields across all layers enables the design of a multi-layer cladding sequence that minimizes the overall residual stress and maximizes the bond quality of each interface.
• Defect Interaction Analysis: Explosion welding can produce defects such as folds, voids, and unmelted zones at the interface. Simulation of the stress field around these defects, combined with the thermal field of a subsequent electric spark welding overlay, can predict whether the overlay will bridge the defect or propagate it. This supports NDT-based acceptance criteria for explosion-welded interfaces.

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

8.1 Qualification Building

Numerical simulation of electric spark welding temperature and stress fields is a powerful tool for building process qualifications. It enables the company to:

• Develop WPS documents with confidence, backed by simulation predictions of dilution ratio, HAZ characteristics, and residual stress levels.
• Reduce the number of PQR trials by narrowing the parameter window for physical testing, thereby accelerating qualification timelines.
• Demonstrate engineering rigor to certification bodies (e.g., ASME, NB, TÜV) by providing simulation-backed justification for parameter selections.
• Extend qualified WPS ranges by using simulation to predict performance at parameter values not covered by physical trials, subject to appropriate safety margins.

8.2 Product Delivery

Simulation supports product delivery by:

• Enabling rapid prototyping and parameter optimization for custom overlay requirements, reducing lead times.
• Providing predictive quality assurance—simulation results can be used to set acceptance criteria for in-process monitoring, ensuring that production parameters remain within the qualified window.
• Supporting root cause analysis when defects occur in production, by comparing actual process conditions with simulation predictions to identify deviations.
• Facilitating the development of overlay solutions for complex geometries and critical applications where physical trial-and-error is impractical or too costly.

8.3 Customer Value

For customers, simulation-backed electric spark welding overlay provides:

• Performance Predictability: Customers can rely on simulation-verified predictions of overlay thickness, dilution ratio, and residual stress levels, reducing the risk of post-installation failure.
• Documentation and Traceability: Simulation results provide a detailed technical record of the overlay process, supporting regulatory compliance and insurance requirements.
• Cost Efficiency: By reducing the number of physical trials and accelerating qualification, simulation lowers the overall cost of overlay solutions for the customer.
• Technical Partnership: The ability to perform rigorous numerical simulation positions Cladding Technology Shanxi Co., Ltd. as a technical partner rather than a simple service provider, enhancing customer trust and long-term business relationships.

9. Conclusion

Numerical simulation of temperature and stress fields in electric spark welding overlay—conducted in both 2D and 3D configurations—represents a critical technical capability for modern cladding and weld overlay manufacturing. It bridges the gap between empirical process knowledge and predictive engineering, enabling the design, qualification, and optimization of overlay processes with greater speed, accuracy, and confidence. For Cladding Technology Shanxi Co., Ltd., this capability strengthens the company's qualification portfolio, accelerates product delivery, and delivers measurable customer value across all three technology routes: TIG/MIG weld overlay, hydraulic explosive bonding, and explosion welding. The integration of simulation with physical qualification, NDT, and quality management systems creates a comprehensive engineering framework that supports the manufacture of high-integrity, high-performance clad and overlay products for critical industrial applications.