CLADDING TECHNOLOGY SHANXI CO., LTDComputer Simulation of Residual Stress Field in Weld Overlay Metals
Literature Overview and Methodological Framework
The research by Yang Qingxiang, Li Yanli, Zhao Yanhui, and Yao Mei, published in the Journal of Welding in 2001, presents one of the earliest comprehensive numerical simulations of residual stress fields in weld overlay metals. This work was supported by the Higher Education Doctoral Point Fund (Grant No. 97021603) and the State Key Laboratory of Modern Welding Production Technology. The authors from Yanshan University's School of Materials Science and Engineering developed a finite element model to predict the residual stress distribution in multi-pass weld overlay layers, providing valuable insights into the stress evolution during the welding process and its implications for overlay layer integrity.
The significance of this research lies in its pioneering application of numerical simulation techniques to weld overlay problems, which were previously addressed primarily through experimental measurement and empirical analysis. The study established a computational framework that could be used to predict residual stress patterns in overlay layers of varying geometries, materials, and process parameters, thereby enabling process optimization and defect prediction before physical welding trials were conducted.
Numerical Model Development and Assumptions
The finite element model employed in this study was based on the coupled thermo-mechanical approach, where the temperature field was calculated first using the moving heat source model, and the residual stress field was then computed by solving the thermo-elastoplastic equilibrium equations. The model incorporated the following key assumptions and material properties:
| Model Parameter | Value / Description | Justification |
|---|---|---|
| Heat source model | Double-ellipsoidal (Goldak) | Accounts for arc penetration and energy distribution |
| Material model | Elasto-plastic with Bauschinger effect | Captures cyclic loading during multi-pass welding |
| Thermal expansion coefficient | Temperature-dependent | Accounts for differential expansion during heating and cooling |
| Yield stress | Temperature-dependent | Accounts for material softening at elevated temperatures |
| Elastic modulus | Temperature-dependent | Accounts for modulus reduction at elevated temperatures |
| Mesh size | 0.5–1 mm near weld pool | Ensures adequate resolution of thermal gradients |
| Element type | 8-node brick (solid) | Standard for 3D welding simulations |
| Boundary conditions | Symmetry and clamped | Simplifies model while capturing essential physics |
The Goldak double-ellipsoidal heat source model was selected because it provides a more realistic representation of the energy distribution in the weld pool compared to simpler point or Gaussian models. The model accounts for the fact that the arc energy is distributed asymmetrically in the direction of travel, with a wider and shallower distribution ahead of the arc and a narrower and deeper distribution behind the arc. This asymmetry is critical for accurately predicting the thermal gradients and residual stress patterns in the overlay layer.
The Bauschinger effect was incorporated into the material model because multi-pass welding involves repeated cycles of heating and cooling, which causes the yield surface to shift and distort. This effect is particularly important in predicting the residual stress state after multiple passes, as it accounts for the fact that the material's yield behavior changes with each thermal cycle.
Simulation Results and Stress Field Analysis
The simulation results revealed that the residual stress distribution in the weld overlay layer was characterized by significant tensile stresses in the weld metal and compressive stresses in the adjacent base metal. The maximum tensile residual stress in the overlay layer was approximately 250–350 MPa, depending on the material properties and welding parameters. The stress distribution was highly non-uniform, with the highest stresses occurring at the weld centerline and decreasing toward the weld edges.
| Position in Overlay Layer | Residual Stress (MPa) | Stress State |
|---|---|---|
| Weld centerline (top surface) | +250 to +350 | Tensile |
| Weld centerline (mid-thickness) | +200 to +300 | Tensile |
| Weld edge (top surface) | +50 to +150 | Tensile |
| Weld edge (mid-thickness) | +100 to +200 | Tensile |
| Base metal (near interface) | -100 to -200 | Compressive |
| Base metal (far from interface) | -50 to -100 | Compressive |
The simulation also revealed that the residual stress state evolved significantly during multi-pass welding. Each subsequent pass introduced new thermal cycles that modified the stress state established by previous passes. The final residual stress distribution was the result of the cumulative effect of all passes, with the later passes having a dominant influence on the stress state near the top surface of the overlay layer.
The effect of welding parameters on the residual stress field was systematically investigated. Increasing the welding current increased the heat input and the magnitude of both tensile and compressive residual stresses. Increasing the travel speed reduced the heat input and generally decreased the magnitude of residual stresses. The deposition thickness per pass also had a significant effect, with thicker passes producing higher residual stresses due to the greater restraint against thermal contraction.
Engineering Implications and Process Optimization
The simulation results have direct implications for the design and optimization of weld overlay procedures. The primary engineering concern is the high tensile residual stress in the overlay layer, which can promote cracking, particularly in materials susceptible to hydrogen-induced cracking (HIC), sulfide stress cracking (SSC), or intergranular stress corrosion cracking (IGSCC). The simulation provides a quantitative basis for evaluating the risk of cracking in overlay layers and for selecting appropriate post-weld heat treatment (PWHT) parameters to relieve the residual stresses.
Based on the simulation results, the following recommendations were made for process optimization: (1) use thin deposition passes (1–2 mm) to minimize the restraint against thermal contraction and reduce residual stresses; (2) employ a multi-pass strategy with alternating welding directions to distribute the thermal cycles more uniformly and reduce the cumulative stress buildup; (3) control the interpass temperature to below 150 °C to promote stress relief during welding; (4) apply post-weld stress relief treatment at 550–650 °C for 2–4 hours to reduce the residual stresses to acceptable levels; and (5) consider using a backing plate or backing bar to provide additional restraint and reduce the magnitude of compressive stresses in the base metal.
The study also demonstrated that the residual stress state could be modified by varying the welding sequence. For example, welding from the center outward produced a different stress pattern than welding from the edges inward. The optimal welding sequence depends on the specific geometry and application, and should be determined through a combination of simulation and experimental validation.
Study Insights and Modern Relevance
This research represents an important milestone in the development of numerical simulation techniques for weld overlay problems. While the computational resources and software capabilities available in 2001 were significantly more limited than those available today, the fundamental methodology and physical insights presented in this study remain highly relevant to modern engineering practice. The coupled thermo-mechanical approach, the Goldak heat source model, and the Bauschinger effect material model are still the standard tools used in contemporary welding simulations.
The key insight from this research is that residual stress prediction is an essential component of weld overlay process development, particularly for applications where cracking resistance is critical. The simulation provides a quantitative basis for evaluating the risk of cracking and for selecting appropriate process parameters and post-weld treatments. While experimental measurement of residual stresses (using X-ray diffraction, neutron diffraction, or hole-drilling methods) remains the gold standard for validation, numerical simulation offers a cost-effective and efficient means of exploring the parameter space and identifying optimal process conditions before physical trials are conducted.
The modern relevance of this research is further enhanced by the availability of advanced computational tools and software packages that can perform three-dimensional, nonlinear, coupled thermo-mechanical simulations with high fidelity and reasonable computational efficiency. Engineers today can leverage the methodology established in this study to develop sophisticated simulation models that incorporate additional physics such as phase transformation, creep, and oxidation, enabling more accurate predictions of residual stress fields in complex weld overlay configurations.
Summary and Concluding Remarks
The five studies reviewed in this document collectively represent significant contributions to the field of cladding, weld overlay, and bimetal product manufacturing. From the comparative evaluation of laser and TIG overlay for cobalt-based alloys, through the microstructural analysis of TIG wire-feed overlay on 2219 aluminum alloy, to the comprehensive review of plasma weld overlay technology, the investigation of rapid laser cladding for corrosion-resistant overlay layers, and the pioneering numerical simulation of residual stress fields, these works provide a rich foundation for understanding the current state of the art and identifying future research directions.
The common thread connecting these studies is the recognition that process parameters, material selection, and microstructural control are the primary determinants of overlay layer quality and performance. Whether the goal is to minimize dilution, optimize microstructure, enhance corrosion resistance, or predict residual stress fields, the systematic approach of combining experimental investigation with numerical simulation and analytical modeling is essential for achieving reliable and repeatable results. As the industry continues to evolve with new materials, new processes, and new applications, the principles and methodologies established in these studies will remain fundamental to the successful development and implementation of advanced cladding and weld overlay technologies.