⚡ electrical engineering

Stage-dependent fracture process zone evolution of mixed mode I-II crack in concrete after low-level sustained loading

This study investigates the stage-dependent evolution of the fracture process zone in mixed mode I-II cracked concrete under low-level sustained loading, revealing that creep induces an early activation followed by a later restriction of crack propagation due to altered structural and local energy states.

Original authors: Maomao Yang, Wei Dong, Wenyan Yuan

Published 2026-10-07

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CC BY 4.0

Original authors: Maomao Yang, Wei Dong, Wenyan Yuan

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Concrete is the most widely used building material on Earth, forming the skeleton of our bridges, dams, and skyscrapers. Yet, like all materials, it is not perfectly uniform; it contains tiny, invisible flaws and microscopic cracks that exist from the moment it hardens. When a structure carries a heavy load for a long time, these hidden imperfections can behave in surprising ways. They do not always grow immediately. Instead, the material can slowly deform, shifting stress around these weak points in a process known as creep. This time-dependent behavior is critical for engineers, who must ensure that a bridge or building remains safe not just today, but decades into the future. The central question is whether a long period of steady, low-level stress changes how the material will eventually break when pushed to its limit.

A team of researchers at Zhejiang University and Dalian University of Technology set out to investigate this specific behavior in concrete beams. They focused on a complex type of cracking where the material is pulled apart and simultaneously sheared, a common scenario in real-world structures that is difficult to predict. To understand this, they needed to look at the "fracture process zone," a region of damaged material just ahead of a crack tip where the concrete is beginning to fail but has not yet separated completely. By observing how this zone evolves after a long period of sustained stress, the researchers hoped to uncover the hidden history of how concrete ages under load.

The experiment began with thirty concrete beams, each carefully cast with a small, pre-existing notch to act as a starting point for a crack. The researchers created five different scenarios for each beam, adjusting the angle of the load to simulate varying degrees of pulling and sliding forces. Half of these beams were left to age naturally in a controlled environment, serving as a baseline. The other half were subjected to a constant, heavy load for ninety days. This load was significant but not enough to cause the beams to break or show visible cracks during the waiting period. After three months, the sustained load was removed, and the beams were immediately tested again until they finally failed.

To see what was happening inside the material, the researchers used a sophisticated imaging technique called digital image correlation. They painted the sides of the beams with a random speckle pattern of black and white dots. As the beams were loaded, high-resolution cameras tracked the movement of these dots, creating a detailed map of how the surface stretched and shifted. This allowed them to measure the tiny movements at the crack tip and determine the exact length of the damaged zone, even before the crack became visible to the naked eye.

The results revealed a story that unfolded in two distinct stages. In the very beginning of the final test, just as the crack started to grow, the beams that had been under sustained load showed a slightly larger damaged zone than the aging beams. It appeared that the long period of stress had "primed" the material, making the crack tip more active and ready to move. However, this early advantage did not last. As the load increased toward the point of failure, the behavior flipped. The damaged zone in the previously loaded beams stopped growing as quickly and ended up significantly shorter than in the beams that had never been stressed. The higher the initial sustained load, the more pronounced this restriction became.

To understand why this happened, the researchers built a computer model that simulated the flow of energy within the concrete. They found that during the ninety-day waiting period, the constant load caused the concrete to slowly deform, absorbing energy in a way that changed the internal state of the material. This energy shift made the crack tip more active initially. But as the final test progressed, the history of that sustained load altered the local energy balance around the crack tip. The material seemed to have less "fuel" available to drive the damage zone forward, causing it to shrink and limiting the extent of the damage right before the beam broke.

This study demonstrates that the history of a structure's loading is not just a record of the past; it actively shapes how the material will fail in the future. A long period of steady stress does not simply weaken concrete uniformly. Instead, it creates a complex, stage-dependent response where the material becomes more susceptible to initial cracking but less capable of sustaining a large zone of damage as it approaches total failure. These findings offer a clearer picture of the time-dependent nature of concrete fracture, suggesting that engineers must account for how a structure's loading history changes its internal energy state to better predict its long-term safety.

Technical Summary: Stage-dependent Fracture Process Zone Evolution of Mixed Mode I-II Crack in Concrete After Low-level Sustained Loading

Problem Statement
Concrete structures often contain initial cracks and imperfections that are subjected to long-term loading. While high-level sustained loading is known to cause progressive crack extension and capacity degradation, the effects of low-level sustained loading (which may not cause visible macro-crack growth) on subsequent fracture behavior remain insufficiently understood. Specifically, the mechanisms governing the evolution of the Fracture Process Zone (FPZ) in mixed mode I-II cracks following such loading history are not fully revealed. Existing research has largely focused on monotonic fracture processes, leaving a gap in understanding how time-dependent deformation, stress redistribution, and localized damage accumulation near the crack tip alter the fracture response during subsequent loading stages.

Methodology
The study employed a combined experimental and numerical approach to investigate the stage-dependent evolution of the FPZ in concrete beams with five different initial mode mixity ratios ( $M_e$ ).

Experimental Program: Thirty single-edge-notched concrete beams ( $500 \times 100 \times 40$ mm) were fabricated. Specimens were divided into "aging" (control) and "creep" groups. Creep specimens were subjected to sustained three-point bending (TPB) or four-point shearing (FPS) loading at two levels ( $0.8P_{ini}$ and $P_{ini}$ , where $P_{ini}$ is the initial cracking load) for 90 days. Following the sustained period, specimens were unloaded and immediately reloaded quasi-statically to failure.
Monitoring: The Digital Image Correlation (DIC) technique was utilized to monitor crack propagation, measuring Crack Mouth Opening Displacement (CMOD) and Crack Mouth Sliding Displacement (CMSD). The FPZ length ( $l_{FPZ}$ ) was identified based on the cohesive crack model, defined as the distance from the physical crack tip to the point where crack opening/sliding displacements reached critical values.
Numerical Modeling: A time-dependent finite element model was established in ANSYS, incorporating the Bailey-Norton creep model and cohesive crack behavior. The model was calibrated against experimental sustained loading data. It was used to analyze global energy evolution (external work, elastic strain energy, and creep strain energy) and local crack-tip average strain energy density ( $\bar{D}$ ) to interpret the experimental observations.

Key Contributions and Results

Macroscopic Fracture Response:
- Low-level sustained loading did not induce visible macro-crack propagation during the 90-day holding period.
- The peak load, initial cracking angle, and macro-crack trajectory remained largely unaffected by the loading history.
- However, the critical crack mouth opening and sliding displacements ( $CMOD_c$ and $CMSD_c$ ) decreased after sustained loading, indicating a reduction in deformation capacity prior to failure.
Stage-Dependent FPZ Evolution:
The study revealed a distinct, non-uniform influence of sustained loading on FPZ evolution, characterized by a transition from early activation to later restriction:
- Early Post-Initiation Phase ( $0.85P_{max}$ ): Creep specimens exhibited FPZ lengths generally comparable to or slightly larger than aging specimens. This suggests that prior sustained loading facilitated the earlier activation of the crack-tip fracture region.
- Middle-to-Late Propagation Phase ( $0.90P_{max}$ to $P_{max}$ ): The trend reversed. The FPZ lengths of creep specimens became smaller than those of aging specimens. This reduction became more pronounced as the sustained loading level increased (e.g., specimens loaded at $P_{ini}$ showed greater reduction than those at $0.8P_{ini}$ ).
- Mode Mixity Influence: Higher shear contributions (lower $M_e$ ) generally resulted in more localized FPZs and shorter lengths at peak load, but the stage-dependent trend of "early activation, later restriction" persisted across all mixity ratios.
Energy-Based Mechanisms:
Numerical analysis provided the physical mechanisms behind these observations:
- Global Energy: During sustained loading, external work and creep strain energy increased continuously, while elastic strain energy remained relatively stable. This accumulation of creep-related energy altered the structural energy state, making the crack-tip region more readily activated during reloading (explaining the early FPZ expansion).
- Local Energy State: During subsequent crack propagation, sustained loading modified the local average elastic strain energy density ( $\bar{D}$ ) around the crack tip. A reduction in $\bar{D}$ was observed in creep specimens compared to aging specimens. This altered local energy state was closely associated with the restricted FPZ development near the peak load.

Significance
The paper claims to improve the understanding of the time-dependent mixed mode I-II fracture behavior of concrete. By demonstrating that sustained loading does not exert a uniform influence but rather induces a transition from early FPZ activation to later restriction, the study highlights the complexity of fracture history effects. The integration of DIC-based experimental characterization with energy-based numerical analysis offers a strategy for revealing the mechanisms governing these time-dependent processes. These findings are essential for evaluating the long-term fracture response of concrete structures, particularly in scenarios where subcritical damage accumulation occurs under low-level sustained loads.

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