Law-dependent Cohesive-Zone Scaling in Mode-I Double-Cantilever-Beam Debonding

Traction–separation laws with the same initial stiffness, strength, and fracture energy can give similar global double-cantilever-beam (DCB) responses but very different process zones. This study quantifies how post-peak law shape affects the debonding-onset process-zone length L0 and its scaling. Six Mode-I laws (rectangular, linear, trapezoidal, finite exponential, quadratic, and multilinear) were compared in 100 Abaqus/Standard simulations spanning strength, fracture energy, arm height, and penalty stiffness, with L0 measured at a common, interpolated onset event. Where a closed-form beam-on-cohesive-foundation solution exists at h = 1.6 mm, linear-law onset loads match it within 1%. Across 16 six-law blocks, the onset-load spread was 1.9–11.8%, whereas the L0 spread was 116–258%, 19–98 times larger, partly owing to the shared fracture energy. The reference-block onset loads lie 11–16% below the beam-theory value, with a deficit that grows with L0. The ranking of L0 never changed, but the fitted exponents depended on the law. Expressed as local slopes of the scaling function, all eighteen estimates fell within the [1/4, 1] bracket of the slender-beam and bulk limits, indicating a shape-dependent crossover governed by the cohesive-length-to-height ratio. Adjacent-point slopes confirm this trend and always separate the largest-area from the smallest-area laws, although area, energy centroid, and final separation vary together. The beam shape coefficient varied with height (coefficient of variation 24–44%), while penalty-stiffness and onset-threshold effects stayed below 1% and 5%. Matching global curves does not ensure local equivalence, and law shape must be considered in parameter identification and mesh design.