Estimation of stress-strain relationship based on localized cracking phenomena for flexure and shear critical reinforced concrete beams under incremental cyclic loading using DIC and AE methods

Reinforced concrete beams under incremental cyclic loading are susceptible to progressive internal damage that conventional load-displacement monitoring cannot adequately resolve. Two critical technical challenges motivate this study. First, for flexural beams, early-stage crack initiation and its quantitative influence on the local strain field must be captured before conventional methods can detect visible crack widths. Second, for shear-critical beams without stirrups, the brittle and sudden nature of diagonal tension failure means that surface measurement techniques cannot resolve the progression of internal damage prior to collapse. This study addresses these challenges through an integrated experimental investigation combining Acoustic Emission (AE) monitoring, Digital Image Correlation (DIC), and a fine-tuned deep learning crack segmentation model (CrackSAM) applied to three reinforced concrete beam specimens under four-point bending. Two large cross-section beams with 250 × 300 mm dimensions were designed for flexural failure (B1) and shear failure without stirrups (B2), and one small cross-section beam with 120 × 150 mm dimensions was designed for flexural failure (B3) to examine size effects. Incremental cyclic loading was applied in three stages corresponding to 30% and 60% of maximum load capacity, followed by monotonic loading to failure. For the flexural beams, a circularity-free decomposition of the DIC-measured longitudinal strain field into a continuum background component and a crack-opening contribution was demonstrated. Crack spatial information was supplied independently by CrackSAM, and the background field was computed from load-cell data and beam theory alone. Where crack detection was successful, the reconstructed field reproduced localized strain concentrations with good fidelity and neutral axis positions agreed well with cracked-section theory. The undetected hairline crack B1–3 in Stage 2 introduced a systematic residual, confirming that complete crack detection is a prerequisite for accurate full-field strain reconstruction. For the shear-critical beam B2, no surface cracks were detected prior to catastrophic failure, and AE monitoring served as the sole means of tracking internal damage accumulation. A sudden concentration of over 4000 AE hits and energy reaching 500 V² was recorded immediately prior to final failure, consistent with the internal propagation of a diagonal tension crack invisible to surface DIC. Stage-dependent evolution of seven AE waveform parameters was evaluated through nonparametric statistical analysis. For the flexural beams, median FRQ-C decreased and RISE and DURATION increased monotonically with loading stage, consistent with progressive microcrack-to-macrocrack transition. For B2, opposing trends were observed, with FRQ-C and P-FRQ increasing progressively, reflecting diagonal crack propagation into less-damaged material. These contrasting directional trends provide a quantitative statistical basis for distinguishing the internal damage signatures of flexural and shear failure modes. Pronounced mechanical size effects were also confirmed, with B3 exhibiting 4.6 times greater ultimate deflection than B1 despite carrying only 15.8% of B1's load capacity, driven primarily by a 94% reduction in the second moment of area. A complete quantitative characterization of the shear failure regime in B2 remains a subject for future work.