Effect of Ligament Length on the Four-Stage Fracture Process of Notched Concrete Beams Under Three-Point Bending

Fracture in concrete is inherently a multi-stage process, yet traditional three-stage frameworks do not explicitly distinguish between micro-crack development and macro-crack propagation, particularly under varying ligament length conditions. The influence of ligament length (notch-to-depth ratios of 0.0, 0.2, 0.3, 0.4, and 0.5) on the crack propagation characteristics in notched concrete beams under three-point bending is investigated. Three-dimensional digital image correlation (3D DIC) was employed to monitor full-field displacement and strain, enabling the evaluation of key fracture parameters including horizontal displacement, crack mouth opening displacement (CMOD), horizontal strain, fracture process zone (FPZ) length, macro-crack length, and total fracture zone length. A high-magnification industrial camera (100×) was simultaneously used for real-time observation of the notch tip. Based on the evolution of these parameters, the fracture process was divided into four distinct stages: linear elastic stage, micro-crack initiation and propagation stage, macro-crack initiation and propagation stage, and complete failure stage. The industrial camera observations confirmed macro-crack initiation at approximately 60% of the post-peak load, validating the proposed four-stage division. Quantitative results show that increasing the notch depth ratio from 0.0 to 0.5 reduces the peak load by approximately 30–40% and decreases the nominal stress proportionally. The FPZ was found to be fully developed at the 60% post-peak load threshold, after which it diminished as macro-crack propagation dominated. Aggregate bridging, crack deflection, and crack branching were consistently identified as the primary toughening mechanisms governing the ligament effect. The crack propagation mechanisms in the four stages are controlled by the combined effects of front free boundary effect, stress concentration effect, ligament effect, and back free boundary effect. These findings provide a refined understanding of concrete fracture that can inform the safety assessment and design of concrete bending members in infrastructure construction.