Mechanics-Based Probabilistic Modeling of Crack-Induced Failures in Glass and Corroded Cables

The presence of cracks and defects in materials plays a critical role in the damage and failure mechanisms of materials and structures, significantly affecting residual strength and durability. Understanding and modeling the propagation of such discontinuities is essential to ensure structural safety, particularly in scenarios involving slow or cumulative loading. This thesis investigates the effect of cracks in two distinct but related contexts, both governed by progressive degradation processes: static fatigue of structural glass and the progressive failure of cables with pitting corrosion. Both phenomena are addressed through probabilistic mechanical approaches, with the aim of improving the understanding of the failure mechanisms and supporting the development of more reliable design criteria. The first part of the thesis investigates static fatigue failure resulting from the subcritical growth of surface cracks in glass panes subjected to wind loads. Most standards reduce the design strength of glass by introducing a modification coefficient kmod in order to account for static fatigue due to subcritical propagation of surface cracks and nominal duration equivalent, in terms of damage, to the actual loading conditions. For wind actions on glass plates, kmod and the nominal durations are based on tradition and practice and are not calibrated from real data. Here, a mechanics-based probabilistic approach is proposed to define modification coefficient and nominal durations based on long-term cumulative wind data relevant to the European context. Wind velocity records from anemometric stations in Italy are used to derive probabilistic distributions, which are incorporated into subcritical crack growth equations to evaluate the modification coefficient as a function of the return period of the wind action. Additionally, kmod is calculated directly through direct integration of available time histories of mean and peak wind velocities. The resulting values are compared with the prescriptions provided by existing design standards. The overall findings are analyzed and interpreted in the concluding section. The second part of the thesis examines the progressive failure of cables composed of wires affected by pitting corrosion, which induces localized pits on the metal surfaces resulting in the formation of cracks and stress concentration/intensification phenomena. The analytical models in the literature typically schematize the cable as a fiber bundle, with the static strength of wires assumed as a random variable and the effect of corrosion introduced according to a strength criterion, thereby neglecting possible brittle fracture mechanics failures. Here, a fiber bundle model made of corroded wires is formulated in order to investigate the critical force-displacement response of the cable, considering both net cross-section and LEFM criteria for the wire's collapse as well as the corrosion variability inside the cable through the introduction of a probability distribution function of the crack depth ratio. Using both criteria allows to introduce a dimensionless group, defined as brittleness number s_e, that controls the transition between brittle and ductile wire failure on varying the damage size and depends on nominal strength, fracture toughness and diameter of the wire. The equilibrium critical load of a cable made of wires that fail by a joint criterion is obtained. The normalized equilibrium load is independent of the nominal strength but it depends on the brittleness number s_e and on the probability distribution of the initial damage. Depending on the value of the brittleness number, the wire failure mode changes from brittle to ductile. As a consequence, the maximum strength and ductility of the cable changes on varying s_e. The effects of the corrosion probability distribution, in terms of its statistical moments, on cable strength and the brittleness number is analyzed. The model is then applied to the Polcevera Viaduct case. The main outcomes and implications of the formulation are discussed in the conclusions.