CPB06 Criterion-Based TA2 Titanium Tee Hydraulic Forming Numerical Simulation

Literature Overview

This study by Sun Lingyan and colleagues from Jiangsu University of Technology, Northwestern Polytechnical University Chongqing Innovation Center, Luoyang Ship Material Research Institute, and Western Superconducting Technologies Co., Ltd. was published in China Materials Progress (2025, Vol. 44, No. 8, pp. 778-784). The research investigates the hydraulic forming of TA2 pure titanium tees using finite element numerical simulation, comparing the Mises isotropic yield criterion with the CPB06 yield criterion to demonstrate the necessity of advanced constitutive models for accurately simulating hexagonal close-packed (HCP) metal forming processes. The work is supported by the National Natural Science Foundation of China (51905233) and a National Defense Basic Research Project (JCKY2020607B003).

Material Characteristics and Modeling Challenge

TA2 pure titanium exhibits a hexagonal close-packed crystal structure with strong basal texture, resulting in pronounced mechanical anisotropy. The key mechanical characteristics include:

• Tensile-compressive asymmetry: The yield stress differs significantly between tension and compression due to the limited number of active slip systems in HCP metals.
• Strong anisotropy: Mechanical properties vary substantially with orientation relative to the texture directions.
• Twist strengthening effect: Significant hardening occurs during twisting deformation modes.
• Limited slip systems: Only three basal slip systems and three prismatic slip systems are available at room temperature, compared to twelve slip systems in FCC metals.

These characteristics make the conventional Mises isotropic yield criterion fundamentally unsuitable for accurately describing the deformation behavior of TA2 titanium during complex forming processes. The Mises criterion assumes isotropic behavior and tension-compression symmetry, both of which are violated by the actual material response.

CPB06 Yield Criterion Advantages

The CPB06 yield criterion was developed specifically to address the limitations of conventional yield criteria for HCP metals. It incorporates:

• Tensile-compressive asymmetry through separate treatment of tension and compression in the yield function.
• Anisotropic hardening behavior that captures the orientation-dependent evolution of yield surface.
• The ability to describe complex stress states encountered during multi-axial deformation in forming processes.

Simulation Results Comparison

The numerical simulation using the Mises criterion produced results that deviated significantly from experimental observations. Most critically, the Mises-based model predicted branch arm collapse—a failure mode that does not occur in actual forming experiments. This prediction error stems from the Mises criterion's inability to capture the actual material flow resistance in the complex stress states present during tee forming.

In contrast, the CPB06-based model accurately predicted:

• Material flow patterns during branch arm formation.
• Wall thickness distribution across the formed tee geometry.
• Stress states in critical regions prone to thinning or wrinkling.
• Physical field evolution behavior throughout the forming process.

The CPB06 model's accuracy enables reliable prediction of forming defects, including thinning locations, potential crack initiation zones, and wrinkling-prone areas. This predictive capability is essential for process optimization and failure analysis in titanium tee manufacturing.

Engineering Practice Implications

For titanium pipe fitting manufacturing, this research highlights several critical points:

1. Constitutive model selection is paramount: Using an inappropriate yield criterion can lead to simulation results that are not merely inaccurate but qualitatively wrong, potentially leading to incorrect process decisions.
2. HCP metals require specialized models: Any forming process involving titanium, magnesium, or zinc alloys should employ yield criteria that account for tension-compression asymmetry and anisotropy.
3. Experimental validation remains essential: Even with advanced constitutive models, simulation results must be validated against physical experiments to ensure model parameters are correctly calibrated.
4. Process optimization requires accurate modeling: The CPB06-based model enables meaningful parametric studies of forming pressure, lubrication conditions, and blank geometry, providing reliable guidance for process development.

Study Insights and Implications

This research serves as a powerful reminder that numerical simulation accuracy is fundamentally limited by the constitutive model's ability to represent real material behavior. In the context of titanium pipe fitting manufacturing, where material costs are high and forming windows are narrow, the use of inappropriate constitutive models can lead to costly process development failures. The CPB06 criterion demonstrates that purpose-built models for specific crystal structures yield dramatically improved simulation fidelity. This principle extends to other advanced materials used in pipe manufacturing—such as nickel-based superalloys, duplex stainless steels, and high-entropy alloys—where conventional isotropic models may similarly fail to capture the true deformation behavior. Engineers must carefully select constitutive models that match the crystal structure and deformation mechanisms of their specific materials to ensure simulation results are both accurate and actionable.