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Updated: Jun 12, 2025
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Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method
Published on: January 16, 2019
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Sprain energy consequences for damage localization and fracture mechanics
Houlin Xu1, Anh Tay Nguyen2, Zdeněk P Bažant1,2,3
1Department of Civil and Environmental Engineering, Northwestern University, Evanston 60208, IL.
Summary
The smooth Lagrangian Crack-Band Model (slCBM) enhances fracture prediction by using "sprain" (second displacement gradient) to limit damage localization. This model accurately captures size effects and outperforms traditional methods, especially under crack-parallel stresses.
Area of Science:
- Computational mechanics
- Materials science
- Fracture mechanics
Background:
- Classical Crack Band Models (CBM) suffer from spurious damage localization.
- Previous models failed to accurately predict fracture behavior under various stress conditions.
Purpose of the Study:
- Introduce and validate the 2023 smooth Lagrangian Crack-Band Model (slCBM).
- Address limitations of existing fracture models, particularly concerning size effects and crack-parallel stresses.
Main Methods:
- Implemented the slCBM using a finite element approach with independent displacement and gradient fields.
- Constrained fields using a second-order Lagrange multiplier tensor.
- Incorporated a constitutive law for triaxial softening damage (microplane model M7).
Main Results:
- slCBM accurately reproduces the size effect observed in the gap test.
- slCBM predictions show significantly less error compared to line crack models, especially with crack-parallel stresses.
- Identified the need to extend localization limiters to include resistance to material rotation gradients.
Conclusions:
- The slCBM effectively prevents spurious damage localization and improves fracture prediction accuracy.
- Existing strain-gradient damage theories may err in fracture patterns and load capacity without considering material rotation gradients.
- The crack-parallel stress effect is a universal phenomenon across different material types.
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