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Background <p>Ultra-thin glass (UTG) has been widely used in high-tech applications due to its flexibility and optical transparency, however, post-processing operations introduce micro-cracks and residual stresses that compromise bending strength. Conventional bending strength definitions often fail to capture actual fracture behavior caused by surface flaws and nonuniform stress distributions.</p> Objective <p>This study aims to develop a general experimental–analytical approach for full-field bending stress evaluation of UTG under two-point bending conditions, capable of accurately describing large deflection behavior and stress evolution along the entire bent profile.</p> Methods <p>Advanced large deflection beam theory (A-LDBT) was applied to the two-point bending configuration, with the horizontal compression distance serving as a single control parameter. A quadratic representation of the deflected beam profile was used to derive the tangent angle along the neutral axis and calculate the full-field bending stress. The analytical profile was verified against bent profile images, while three-dimensional digital image correlation (3D-DIC) provided full-field strain measurements under various compression distances.</p> Results <p>The deflection beam profile equation successfully determined the geometric parameters, and experimental strain distributions agreed well with theoretical predictions from A-LDBT. Despite setup limitations, 3D-DIC captured local strain fields at critical bending locations. The measured strains enabled direct evaluation of bending stress without relying on contour extraction or repeated curve fitting.</p> Conclusions <p>The results demonstrate that combining A-LDBT with 3D-DIC provides a reliable method for full-field stress evaluation of UTG under two-point bending. By removing previous contact angle restrictions, the approach extends the measurable deformation range and enables effective assessment of stress and mechanical reliability in UTG substrates.</p>

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Full-Field Two-Point Bending Stress Evaluation by Advanced Large Deflection Beam Theory

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月28日

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  • F.-J. Wang,
  • P.-C. Sung,
  • W.-C. Wang,
  • C.-H. Chang,
  • Y.-W. Kuo

摘要

Background

Ultra-thin glass (UTG) has been widely used in high-tech applications due to its flexibility and optical transparency, however, post-processing operations introduce micro-cracks and residual stresses that compromise bending strength. Conventional bending strength definitions often fail to capture actual fracture behavior caused by surface flaws and nonuniform stress distributions.

Objective

This study aims to develop a general experimental–analytical approach for full-field bending stress evaluation of UTG under two-point bending conditions, capable of accurately describing large deflection behavior and stress evolution along the entire bent profile.

Methods

Advanced large deflection beam theory (A-LDBT) was applied to the two-point bending configuration, with the horizontal compression distance serving as a single control parameter. A quadratic representation of the deflected beam profile was used to derive the tangent angle along the neutral axis and calculate the full-field bending stress. The analytical profile was verified against bent profile images, while three-dimensional digital image correlation (3D-DIC) provided full-field strain measurements under various compression distances.

Results

The deflection beam profile equation successfully determined the geometric parameters, and experimental strain distributions agreed well with theoretical predictions from A-LDBT. Despite setup limitations, 3D-DIC captured local strain fields at critical bending locations. The measured strains enabled direct evaluation of bending stress without relying on contour extraction or repeated curve fitting.

Conclusions

The results demonstrate that combining A-LDBT with 3D-DIC provides a reliable method for full-field stress evaluation of UTG under two-point bending. By removing previous contact angle restrictions, the approach extends the measurable deformation range and enables effective assessment of stress and mechanical reliability in UTG substrates.