Numerical Simulation of Martensitic Transformation Effect on Cooling Tangential Stress in Weld Overlay

Literature Overview and Research Background

This study addresses a critical yet often underappreciated aspect of weld overlay engineering: the contribution of martensitic phase transformation to the residual stress field, particularly the tangential (circumferential) stress component, during the cooling phase of overlay welding. In cladding operations where martensitic stainless steels or high-hardness martensitic alloys are deposited, the austenite-to-martensite transformation introduces volumetric expansion that superimposes upon the thermally induced contraction. The resulting stress state governs crack susceptibility, cladding-to-base-metal bond integrity, and the long-term dimensional stability of the overlay. The numerical approach adopted in this work employs finite element analysis (FEA) coupled with a thermomechanical constitutive model that explicitly accounts for phase transformation strain, making it a significant advancement over purely thermal-elastic models.

Core Technical Content

The fundamental premise of the study is that martensitic transformation strain is not merely an additive perturbation to the thermal stress field but rather a dominant contributor to the tangential stress component in the cooling stage of overlay welding. The transformation strain arises from the crystallographic change from face-centered cubic (FCC) austenite to body-centered tetragonal (BCT) martensite, which involves a lattice parameter change of approximately 0.004 mm in the c/a direction and a corresponding volumetric expansion of 0.5–1.5% depending on the carbon content of the alloy.

Numerical Model Configuration

Key Findings on Tangential Stress Distribution

The study reveals several important findings that directly impact engineering practice:

1. Tangential stress amplification: The martensitic transformation can increase the peak tensile tangential stress by 30–60% compared to a purely thermal-elastic prediction. This amplification is most pronounced in the region immediately adjacent to the cladding interface, where the cooling rate is highest and the transformation temperature is lowest.
2. Cooling rate sensitivity: At cooling rates above approximately 20 °C/s, the transformation strain becomes the dominant stress contributor. Below 10 °C/s, the thermal component dominates because the transformation is retarded and occurs at higher temperatures where the yield strength is lower.
3. Multi-pass effects: In multi-pass overlay sequences, the thermal history of previously deposited layers modifies the transformation temperature and kinetics of subsequent passes. The simulation demonstrates that the cumulative transformation strain across multiple passes can lead to a net compressive stress state near the substrate surface, which is beneficial for bond integrity.
4. Crack susceptibility correlation: The predicted peak tensile tangential stress correlates well with experimentally observed crack initiation locations. Regions where the simulated tangential stress exceeds the fracture toughness threshold of the martensitic microstructure (typically K_IC ≈ 30–50 MPa·m^0.5 for untempered martensite) correspond to observed cold cracking zones.

Interpretation of Technical Points

Transformation Strain Mechanism

The Koistinen-Marburger equation used in the model expresses the martensite volume fraction as:

V_m = f(V_f) × (1 - exp(-β(T_s - T)))

where V_f is the final martensite fraction, T_s is the martensite start temperature, T is the current temperature, and β is a material constant related to the transformation kinetics. The key insight is that the transformation strain is not uniform throughout the weld cross-section because the cooling rate varies radially and axially. This non-uniformity creates internal stress gradients that are particularly severe in the tangential direction due to the geometric constraint imposed by the cylindrical or flat geometry.

Comparison with Experimental Data

The study validates the numerical predictions against experimental measurements obtained through X-ray diffraction and hole-drilling methods. The agreement is generally within 15–20% for the peak stress magnitude, which is considered acceptable given the inherent uncertainties in material property inputs and boundary condition idealizations.

Engineering Practice Implications

Process Optimization Strategies

Based on the simulation results, several practical recommendations emerge for overlay welding engineers:

• Preheating: Increasing the substrate preheat temperature from 50°C to 150°C reduces the peak cooling rate by approximately 30%, shifting the transformation to higher temperatures where the yield strength is lower and the transformation strain is partially relieved by plastic deformation.
• Interpass temperature control: Maintaining interpass temperatures between 100–200°C for martensitic overlays ensures that the previously deposited layers remain above the martensite finish temperature (M_f) during subsequent passes, allowing transformation strain relaxation through creep and plastic flow.
• Post-weld heat treatment (PWHT): A tempering treatment at 500–650°C for 1–2 hours can relieve up to 70–80% of the transformation-induced residual stress while simultaneously improving the toughness of the martensitic microstructure.

Design Considerations for Clad Pressure Vessels

For bimetallic pressure vessels fabricated with martensitic stainless steel overlays (such as those used in hydrogen service or high-temperature sour environments), the tangential residual stress field directly affects the fatigue life and stress corrosion cracking (SCC) susceptibility. According to ASME VIII Div.1 and NB/T 47002 requirements, the residual stress must be evaluated when the overlay thickness exceeds 50% of the total wall thickness. The numerical approach presented in this study provides a rigorous method for such evaluation that can be incorporated into fitness-for-service (FFS) assessments.

Key Questions and Reflections

The most thought-provoking aspect of this study is the recognition that conventional residual stress prediction methods, which rely solely on thermal-elastic-plastic models, systematically underestimate the tangential stress in martensitic overlays. This has implications for existing design codes and qualification procedures. If the actual residual stress field is significantly more severe than what is predicted by standard methods, then the current acceptance criteria for cladding welds may be insufficiently conservative.

Furthermore, the study highlights the importance of accurate material property data at elevated temperatures. The transformation strain magnitude is sensitive to the carbon content and the cooling rate, both of which are process-dependent variables. In practice, this means that the residual stress field in a given overlay can vary substantially depending on the welding parameters, even when the nominal heat input is held constant.

Study Insights and Conclusions

This literature provides a compelling demonstration that the martensitic transformation is not a secondary effect in weld overlay residual stress prediction but rather a primary driver of the tangential stress component. The numerical methodology developed here offers a powerful tool for process optimization, defect prediction, and design validation in cladding applications involving martensitic materials. For engineers involved in the fabrication of clad pressure vessels, hydrogenation reactors, and other critical equipment using martensitic overlay alloys, the key takeaway is clear: residual stress management must explicitly account for phase transformation effects, and the cooling rate and interpass temperature must be carefully controlled to minimize transformation-induced stress concentrations. Future work should extend this approach to three-dimensional geometries and multi-layer multi-pass sequences to capture the full complexity of industrial overlay operations.