Development of computational models for fracture analysis of engineering materials: Application in adhesively and cementitious composites

Abstract

Composites have become the material of choice in aerospace, marine, and structural engineering due to their exceptional strength-to-weight ratio and design flexibility. Laminated composites and sandwich composite structures are widely employed in these sectors. Reinforced cement concrete is another composite commonly used in civil and structural infrastructure construction, such as buildings and bridges. These materials are typically fabricated by combining multiple constituents that complement each other and bond together using adhesives (two compound systems) or chemical hydration processes. However, the performance of a composite is fundamentally reliant on the integrity of its weakest component, as encapsulated by the adage, "A chain is only as strong as its weakest line." This phenomenon is illustrated in composite laminates, where interlaminar bonding significantly influences stiffness and failure strength, with shear stress causing delamination. While linear analysis often assumes perfect bonding, this assumption is unrealistic at increased loads. Similarly, in sandwich panels, the interface between the core and skins is a critical region prone to delamination under various loading conditions. Likewise, In short steel fiber reinforced concrete, the ability to bridge cracks is crucial, but the excessive load can lead to fiber pullout due to interfacial bond failure. These examples underscore the need to capture interfacial behavior to predict composite performance and failure accurately. This thesis investigates the critical interplay between interfacial bonding and constituent materials'"intrinsic properties in determining composite systems" overall behavior and failure mechanisms. Composite structures such as laminates and sandwich panels often exhibit the mechanical behavior of plates, shells, or beams. However, in literature, most existing failure models are formulated for continuum elements in two or three dimensions. This research presents a novel beam-based discrete cohesive zone model to address the computational challenges associated with continuum-based models for composite structures. The proposed model discretizes the adherent using beam elements and represents the adhesive as discrete springs whose stiffness and fracture parameters are calibrated to cohesive zone parameters. This approach significantly enhances computational efficiency for thin composite laminates. The model's accuracy is validated against experimental data for Mode I, Mode II, and mixed-mode loading conditions. Furthermore, the model is extended to simulate delamination in sandwich panels by employing higher-order beam theory for theskins" core and Timoshenko beam elements. The model's predictive capabilities are compared with available experimental data for Mode I and II delamination. If the adhesive bond between the core and skin is stronger than the core material, core failure often becomes the predominant failure mode in sandwich panels. These cores typically consist of periodic or irregular arrangements of interconnected structural elements known as unit cells. The term architected lattice material (ALM) is often used to describe these structures collectively. A beam-based phase-field damage model has been developed to analyze the fracture behavior of ALM grids. The model is formulated by coupling the kinematics of Timoshenko beam theory with brittle phase-field damage modeling principles. This approach significantly reduces the computational cost by decreasing the degrees of freedom by over 95%, leading to a more than 99% computational speedup. The model's stability is demonstrated through simulations of thin and thick beam-based ALMs, with results showing good agreement with available experimental data. Building upon the work on interfacial modeling between material and bulk material failure within architected lattice material (ALM) grids, a quasi-brittle phase field-based damage model for short fiber reinforced composites is developed. Steel fiber reinforced concrete (SFRC) is employed as a case study. The model incorporates randomly distributed steel fibers within a macroscale homogenized concrete matrix, with fibers represented as two-dimensional truss elements. A traction-separation law governs the fiber-concrete interface, while the concrete matrix is modeled using a quasi-brittle phase-field damage approach. The model effectively simulates the classical three-point bending test for SFRC with varying fiber contents (0%, 0.5%, 1%, and 2%), demonstrating good agreement with experimental data. Due to the macroscale representation of the concrete matrix, the model is extended to high-strength steel fiber reinforced concrete (HS-SFRC) by adjusting the material properties of the concrete. The model successfully replicates three-point bending behavior for HS-SFRC as well. An L-shaped mixed-mode problem is simulated for SFRC to assess model robustness, demonstrating the model's ability to handle complex loading conditions. Overall, this study presents the development of a theoretical framework to efficiently reduce the computational complexity in simulating the load deformational response of reinforced composites subject to diverse loads.