Fractal Evolution of DIC-Derived Tensile Strain Localization in CNT–Recycled Steel Fiber Cementitious Composites Under Sulfate Dry–Wet Cycles

Sulfate dry–wet cycling can progressively alter the tensile damage mode and self-sensing behavior of conductive fiber-reinforced cementitious composites, whereas conventional strength indices cannot fully describe the spatial organization of damage. In this study, nine carbon nanotube–recycled steel fiber (CNT–RSF) cementitious composites were first evaluated by direct tensile testing, after which the B2 mixture containing 0.3% CNT and 1.25 vol.% RSF was selected for detailed digital image correlation (DIC)-based fractal analysis. The high-strain area ratio RA and box-counting fractal dimension DB were introduced to characterize the spatial extent and geometrical complexity of tensile localization, respectively. B2 exhibited the best overall tensile-strength retention, reaching 105.8%, 99.2%, and 83.7% after 50, 100, and 150 sulfate dry–wet cycles. For the representative B2 specimen after 100 cycles, RA increased to 0.1607 at final failure, whereas DB increased to a maximum of 1.492 and subsequently decreased to 1.424, indicating late-stage geometrical reorganization from distributed localization toward dominant failure. Persistent localization occurred at ξloc ≈ 0.20, while maximum fractal complexity was reached later at ξD,max ≈ 0.73. A comparison between the 0- and 150-cycle states showed that peak tensile stress decreased by approximately 21.4%, whereas the peak-state and terminal fractional changes in resistance decreased by approximately 30.4% and 37.4%, respectively. SEM observations further provided qualitative microstructural support for the transition from distributed load transfer to concentrated fracture-controlled deformation. These results indicate that the combined RA–DB framework provides complementary spatial information beyond conventional tensile-strength measurements and may offer a useful approach for characterizing environmentally induced tensile damage in self-sensing cementitious composites.