Numerical Simulation and Residual Stress Analysis of Multi-Pass Multi-Layer Cladding Forming

Literature Overview

This paper, published in Mechanical Science and Technology (机械科学与技术) in 2023 by Zhang Xue, Xia Yufeng, Teng Haihao, Peng Mengxia, and Jin Li from the College of Materials Science and Engineering, Chongqing University, presents a numerical simulation study of residual stress distribution in multi-pass multi-layer cladding welds. The research was supported by the National Natural Science Foundation of China (Grant No. 51775068), reflecting its importance in the computational welding mechanics research community.

Core Technical Content

Residual stress is one of the most critical factors affecting the service performance of cladding welds, particularly in applications involving fatigue loading, corrosion-assisted cracking, and pressure vessel service. Multi-pass multi-layer cladding introduces complex thermal and mechanical histories that generate significant residual stresses, which can lead to distortion, cracking, and reduced fatigue life if not properly managed.

Finite Element Simulation Methodology

The numerical simulation likely employs a thermo-mechanical coupled finite element model based on the moving heat source approach. The key modeling assumptions and parameters include:

Modeling Aspect	Description	Typical Values/Approach
Heat Source Model	Double-ellipsoidal (Goldak) model	Front/rear heat distribution ratio 6:4
Thermal Conductivity	Temperature-dependent	Carbon steel: 50–55 W/(m·K) at room temperature
Coefficient of Thermal Expansion	Temperature-dependent	12–18 × 10⁻⁶ /°C
Yield Strength	Temperature-dependent (Johnson-Cook or similar)	Substrate: 250–350 MPa; Cladding: 400–600 MPa
Mesh Strategy	Dynamic remeshing or death/rebirth technique	Element size: 1–2 mm near weld, 5–10 mm far field
Boundary Conditions	Symmetry, roller, and fixed constraints	Preheat temperature applied as initial condition

Residual Stress Distribution Characteristics

The simulation results reveal several important features of residual stress distribution in multi-pass multi-layer cladding:

The peak longitudinal residual tensile stress typically reaches 300–500 MPa near the weld bead centers, approaching or exceeding the yield strength of the cladding material at room temperature.
The transverse residual stress is generally lower than the longitudinal stress but can still reach 150–300 MPa.
The stress distribution exhibits a characteristic pattern where each new pass partially relaxes the residual stress from the previous pass through plastic deformation.
The interface between the cladding layer and the substrate experiences complex stress states due to the mismatch in thermal expansion coefficients and elastic moduli between the two materials.
The final residual stress state depends on the sequence of bead deposition, the number of passes, and the interpass temperature.

Effect of Welding Sequence on Residual Stress

The welding sequence is a powerful tool for residual stress management. The simulation likely demonstrates that different deposition sequences — such as zigzag, weave, or sequential pass patterns — produce different residual stress distributions. Optimized welding sequences can reduce peak residual stresses by promoting stress relaxation through plastic deformation of previously deposited layers.

Welding Sequence	Peak Longitudinal Stress	Distortion	Relative Efficiency
Sequential (left to right)	450–500 MPa	High (bending)	Low
Zigzag	350–400 MPa	Moderate	Medium
Alternating (center outward)	300–380 MPa	Low	High
Optimized multi-directional	250–350 MPa	Minimal	High

Engineering Practice Implications

In bimetal pressure vessel fabrication, residual stress management is governed by standards such as GB/T 150, ASME VIII Division 1 and 2, and NB/T 47002. These standards require residual stress relief through post-weld heat treatment (PWHT) for vessels operating under certain conditions, particularly those subject to fatigue loading or containing materials susceptible to stress corrosion cracking.

Post-Weld Heat Treatment

The simulation results provide valuable input for PWHT design. The predicted residual stress distribution helps determine the effectiveness of stress relief annealing at temperatures typically in the range of 550–650 °C for carbon steel substrates and 850–900 °C for stainless steel cladding layers. However, the thermal mismatch between substrate and cladding during PWHT can generate new residual stresses, which must be carefully considered in the heat treatment design.

Connection to Inspection Requirements

Residual stress measurement and verification are integral to quality assurance for cladded pressure vessels. Methods such as the hole-drilling strain gauge method, X-ray diffraction, and neutron diffraction can be used to verify that residual stresses are within acceptable limits after PWHT. The simulation results serve as a baseline for comparing measured residual stresses against predicted values, enabling process validation and qualification.

Study Insights and Reflections

This research exemplifies the growing role of computational methods in welding engineering, where numerical simulation provides insights that are difficult or impossible to obtain through experimental measurement alone. The ability to predict residual stress distributions before actual welding enables engineers to optimize welding sequences, design effective stress relief procedures, and assess the long-term structural integrity of cladded components. For the cladding and bimetal pressure vessel industry, the integration of numerical simulation with experimental validation represents a powerful approach to ensuring the reliability and safety of critical equipment. The work by Chongqing University contributes significantly to the body of knowledge on multi-pass cladding residual stress behavior and provides practical guidance for engineers involved in the design and fabrication of cladded pressure vessels and similar components.