Two-Dimensional and Three-Dimensional Numerical Simulation of Temperature and Stress Fields in Spark Cladding

Literature Overview

This study presents a comprehensive numerical simulation approach for modelling the transient thermal and mechanical fields generated during electric spark cladding (ESC), also known as electric arc surfacing or pulsed arc cladding. The work addresses the fundamental challenge of predicting residual stress distributions and microstructural evolution in overlay deposits by employing both two-dimensional and three-dimensional finite element models. The research is particularly relevant to engineers involved in bimetal pressure vessel fabrication and corrosion-resistant cladding applications where residual stress control is critical to long-term structural integrity and resistance to stress corrosion cracking.

Core Technical Approach

The simulation framework is built upon coupled thermo-mechanical finite element analysis using sequential coupling methodology. The thermal analysis employs a moving heat source model that characterises the pulsed nature of the electric arc, while the mechanical analysis incorporates plastic deformation and creep effects during the cooling phase. The key modelling parameters include the arc power input, pulse frequency, scanning speed, and the volumetric energy density distribution.

The two-dimensional model simplifies the geometry by assuming plane strain conditions, which significantly reduces computational cost while still capturing the essential thermal gradients in the depth direction. However, the three-dimensional model is essential for capturing the full spatial variation of the thermal field, particularly at the leading and trailing edges of the weld bead where significant three-dimensional effects arise. The study demonstrates that the 3D simulation results show peak residual stresses approximately 15 to 25 percent higher than the 2D predictions in the transverse direction, highlighting the necessity of three-dimensional modelling for accurate residual stress assessment in engineering practice.

Key Technical Findings and Interpretation

The temperature field analysis reveals that the peak temperature at the arc contact point can exceed 2500 °C, with rapid cooling rates reaching values between 100 and 500 °C/s in the solidification zone. These high cooling rates are responsible for the formation of fine-grained microstructures in the overlay deposit, which contribute to improved mechanical properties. The stress field analysis identifies the presence of compressive residual stresses in the near-surface region, transitioning to tensile stresses in the mid-depth zone. This stress distribution pattern is consistent with the thermal contraction sequence during solidification and cooling.

The study further examines the influence of process parameters on residual stress magnitude and distribution. Increasing the scanning speed results in lower peak temperatures and reduced heat input, which leads to higher cooling rates and consequently increased residual stresses. Conversely, higher arc power increases the heat input but also increases the melting penetration depth, which can partially relax residual stresses through thermal plasticity. The optimal parameter window for minimising residual stress is identified as a balance between moderate arc power and moderate scanning speed.

Integration with Engineering Practice

In the context of bimetal pressure vessel fabrication, residual stress management is of paramount importance. According to NB/T 47002 and ASME VIII Div.1, the residual stress level directly affects the fatigue life and stress corrosion cracking resistance of the cladding layer. For austenitic stainless steel cladding layers on carbon steel substrates, residual tensile stresses exceeding 200 MPa can significantly reduce the threshold for chloride-induced stress corrosion cracking. The simulation results provide valuable guidance for post-weld heat treatment (PWHT) parameter selection, as the predicted stress distribution can be used to optimise the PWHT temperature and duration.

The practical implication is that engineers can use the simulation-derived stress maps to determine whether PWHT is necessary or if stress-relief can be achieved through process parameter optimisation alone. For critical applications such as hydrogenation reactors and high-pressure hydrogen service, the combination of simulation-based prediction and experimental validation through X-ray diffraction or neutron diffraction residual stress measurement is recommended.

Study Insights and Reflections

The most significant insight from this literature is the quantitative demonstration that 3D modelling is not merely an academic exercise but a practical necessity for accurate residual stress prediction in spark cladding applications. The 15 to 25 percent discrepancy between 2D and 3D predictions in peak stress values can mean the difference between an acceptable and an unacceptable residual stress state for stress corrosion cracking-sensitive applications. Furthermore, the coupled thermo-mechanical approach captures the non-linear material behaviour during the solidification and cooling phases, which is essential for realistic stress predictions.

A limitation identified in the study is the simplification of the material constitutive model, which assumes isotropic elastic-plastic behaviour without accounting for anisotropy induced by solidification texture. Future work should incorporate crystal plasticity models to capture the anisotropic deformation behaviour of columnar grain structures typical of weld overlay deposits. The engineering value of this study lies in providing a validated simulation framework that can be adapted for specific cladding systems and process conditions, thereby reducing the reliance on expensive and time-consuming experimental residual stress measurement campaigns.