Finite Element Simulation of Medium-Frequency Heated Large-Diameter Steel Pipe Bending Process

Literature Overview

The paper by Xu Zhiqiang, Li Xuetong, and Du Fengshan from Yanshan University, published in the Journal of Yanshan University in 2003 (Vol. 27, No. 2, pp. 122-125), addresses a critical manufacturing challenge in large-diameter steel pipe forming: the medium-frequency induction-heated push bending process. Funded by the National Natural Science Foundation of China (Grant No. 5007507), this study employs elastoplastic large-deformation finite element theory on the MARC platform to build a coupled thermo-mechanical model of the bending process. The authors specifically leverage the user subprogram capability of MARC to simulate the localized medium-frequency heating zone, a feature that distinguishes their approach from conventional uniform heating simulations.

Core Technical Content and Methodology

The central technical contribution lies in the coupled thermal-stress finite element model that captures the complex interaction between localized induction heating and plastic deformation during bending. Unlike conventional hot bending where the entire pipe circumference is uniformly heated, medium-frequency heating targets only a narrow band around the bending zone, which creates a steep thermal gradient and highly non-uniform material softening. The authors model this using MARC's open architecture, writing custom user subroutines to define the spatially varying temperature field and corresponding material properties at each integration point.

The elastoplastic constitutive model accounts for temperature-dependent yield strength, strain hardening behavior, and thermal expansion of the steel pipe material. During the bending simulation, the loading sequence mimics the actual push-bending operation where the heated section of the pipe is progressively deformed by a mandrel or roller system. The output parameters analyzed include cross-sectional shape evolution, wall thickness distribution, metal flow patterns, and residual stress states.

Key Technical Points and Process Parameters

The simulation reveals that the maximum wall thinning occurs at the inner fiber of the bend, with thinning rates ranging from 5% to 15% depending on the bend radius-to-diameter ratio. The cross-section tends to ovalize under bending, with the degree of ovalization increasing as the bend angle increases. Metal flow analysis shows that material from the outer fiber migrates inward, creating a densification zone that partially compensates for wall thinning but introduces non-uniform thickness distribution.

Engineering Practice Implications

From a manufacturing standpoint, the simulation results provide a rational basis for selecting bend radii, heating parameters, and tooling configurations. In practice, large-diameter pipes (typically D > 600 mm) used in pipeline networks, structural applications, and marine engineering frequently require bending operations. The localized heating approach offers significant energy savings compared to full-circumference heating, but it introduces challenges in temperature control and deformation uniformity that must be carefully managed.

The study highlights that the thermal gradient between the heated zone and the adjacent cold material creates a constraint effect that can either limit deformation or, if poorly controlled, lead to cracking. The user subprogram approach demonstrated here provides a methodology that can be adapted for other localized heating scenarios, such as flash butt welding preheating or local annealing operations.

Critical Reflection and Study Insights

The 2003 publication date reflects an era when finite element simulation of forming processes was still maturing in industrial applications. While the coupled thermo-mechanical approach is sound, modern practice would benefit from incorporating more sophisticated material models that account for microstructural evolution during heating and cooling. The simulation also does not address post-forming residual stress relaxation through stress relieving heat treatment, which is a critical consideration in high-pressure pipeline applications governed by standards such as ASME B31.3 and API 5L.

The user subprogram methodology, while effective for its time, has been largely superseded by more integrated multiphysics simulation tools. However, the fundamental insight that localized heating creates a complex thermomechanical coupling that cannot be adequately captured by simplified models remains highly relevant. For engineers currently working on large-diameter pipe bending operations, this paper serves as a foundational reference that validates the necessity of full coupled analysis over decoupled thermal and mechanical simulations.

The paper's practical value lies in its demonstration that finite element simulation can reliably predict deformation patterns and thickness distributions, enabling process optimization before physical trials. This reduces trial-and-error costs and accelerates production ramp-up for new pipe specifications.