Date of Award
5-2025
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Aerospace, Physics, and Space Sciences
First Advisor
Mirmilad Mirsayar
Second Advisor
Soheil Saedi
Third Advisor
Manasvi Lingam
Fourth Advisor
Ratneshwar Jha
Abstract
The quest for safety, efficiency, and innovation in aerospace engineering demands a relentless focus on understanding how materials and structures behave under extreme and complicated loading conditions. Among the many challenges faced by engineers in this field, predicting and preventing structural failure stands out as both a fundamental necessity and a complex problem. Fracture mechanics, the science of how materials fail under stress, is a cornerstone of this effort. Whether it is the fuselage of an aircraft enduring cyclic loading or the lightweight components of a spacecraft resisting impact, the ability to accurately predict fracture behavior directly influences the reliability and performance of aerospace systems. This dissertation contributes to that critical endeavor by advancing fracture mechanics in two distinct yet interconnected domains: the development of more accurate fracture criteria using the Effective Critical Distance (ECD) approach, and the exploration of fracture behavior in microcellular materials. These advancements are grounded in a series of peer-reviewed published papers that form the core of this work, reflecting years of theoretical development, computational modeling, and experimental validation. This dissertation is structured around two main chapters, each built upon peer-reviewed papers published during this doctoral study. By incorporating these papers directly into the dissertation, we aim to present a comprehensive and transparent account of our contributions to the field. The importance of this research cannot be overstated. Fracture mechanics has long been a vital discipline in aerospace engineering, where the consequences of material failure can be catastrophic. The ability to predict when and how a crack or notch will propagate allows engineers to design structures that are both safe and efficient, balancing the competing demands of strength, weight, and cost. The current doctoral dissertation is positioned at the intersection of fracture mechanics and the emerging domain of microcellular materials, exploring fundamental enhancements to fracture criteria and novel insights into fracture mechanics in structured porous media. The first chapter of this dissertation addresses a fundamental limitation of classical fracture mechanics: the oversimplified treatment of the critical distance parameter. Historically, fracture criteria have employed a critical distance defined under pure Mode I loading conditions, assuming mode independence. This simplification, while convenient, has proven insufficient for accurately predicting real-world mixed-mode fracture scenarios, particularly in three-dimensional brittle fractures involving complex stress fields. In response, the current research utilized the Effective Critical Distance (ECD), a mode-dependent approach capable of capturing nuanced variations in critical distance across different modes of loading to enhance the accuracy of fracture criteria in both cracked and notched components. In Section 1.1, we demonstrated the application of ECD in cracked specimens under mixed-mode I/II/III loading conditions. Utilizing an energy-based framework, we introduced a novel criterion called ECD-MTSED which combines ECD with maximum tangential strain energy density. The results clearly illustrated significant improvements in prediction accuracy compared to traditional criteria, thereby validating the efficacy of the ECD approach in capturing realistic three-dimensional fracture behaviors. This advancement not only provides a more precise theoretical model but also simplifies practical fracture assessments by reducing reliance on extensive experimental calibration. Section 1.2 further extended the concept of ECD to notched components, prevalent in structural designs due to their functional necessity in load transfer and structural connections. Recognizing that notches represent inherently more complex stress raisers than cracks, we introduced a new fracture criterion based on maximum principal strain (MPSN) integrated with ECD for predicting mixed-mode fracture in V- and U-shaped notches. Comparative analyses with experimental data underscored the superior predictive capability of this new criterion, further validating the universal applicability and precision of the ECD concept. These findings provide critical insights into fracture initiation and propagation around structural discontinuities, essential for safer and more reliable design methodologies. Completing the first chapter, Section 1.3 presented extensive experimental work through fracture tests on Polyurethane (PUR) foams subjected to mixed-mode I/II and I/III loading conditions. Using edge-notched disc bend specimens, we generated original experimental data, including fracture toughness values and fracture initiation angles. Applying the ECD-based strain criterion, ECD-SN, we demonstrated significantly improved predictive accuracy over existing fracture criteria. The successful experimental validation reinforced the theoretical robustness of ECD and provided practical guidance for engineers working with porous polymeric foams, a widely used class of lightweight materials in industry. Transitioning to the second chapter, the current research delved deeply into the complex fracture behaviors of microcellular structures. These materials, characterized by their void-solid structures, are increasingly favored due to exceptional strength-to-weight ratios and their customizability for specific applications. However, traditional fracture mechanics frameworks face significant challenges when applied to these inherently discontinuous materials, necessitating novel approaches and advanced computational methods. Section 2.1 serves as a comprehensive introduction to microcellular materials in the second chapter, providing an extensive literature review and detailed analysis of the fracture mechanics of cellular structures, highlighting past achievements, current research trends, and identifying critical knowledge gaps. This section specifically emphasizes the limited understanding and exploration of fracture behavior in additively manufactured functionally patterned microcellular materials. While the mechanics of these materials have been investigated, particularly in constitutive behavior and structural optimization, their fracture behaviors under complex loading conditions remain inadequately explored. Our critical assessment identified the necessity of accurately modeling microcellular structures as continuous media to facilitate the application of fracture mechanics principles. This foundational review highlighted key knowledge gaps, particularly the limited understanding of mixed-mode fracture behavior in additively manufactured functionally graded microcellular materials. By clearly articulating these gaps and opportunities, this review established a theoretical baseline and set the stage for the systematic experimental and computational investigations detailed in subsequent sections of this chapter. Building on these insights, Section 2.2 describes the development of a sophisticated numerical homogenization approach tailored explicitly for periodic orthotropic functionally graded microcellular materials. The homogenization methodology introduced in the current research uniquely accommodates both solid-phase orthotropy (caused by additive manufacturing processes) and geometrically induced anisotropy in the homogenization calculations. Implemented through custom-developed MATLAB codes, this homogenization procedure provides an accurate elasticity tensor in which each entry is a function of spatial coordinates, mapping the entire material domain. This specific output is particularly useful, as it can be utilized in advanced fracture models. Moreover, such tools enable engineers and researchers to accurately predict macroscopic mechanical behavior without the computational intensity of discrete modeling, bridging microscale features with macroscale analysis. In Section 2.3, we systematically performed experimental fracture analyses of 3D-printed ABS microcellular specimens characterized by periodic orthotropic functionally graded structures containing circular voids. Our study systematically investigated the influence of critical parameters including orthotropy angle (printing angle), void distribution pattern, and initial crack position (within the solid phase versus aligned with void rows) on fracture initiation, crack propagation paths, and fracture strength. Utilizing tensile mechanical testing, we captured detailed load-displacement responses and closely observed crack behaviors, revealing that cracks predominantly initiate along the printing direction due to inherent material orthotropy. However, upon encountering voids, crack tips notably blunt, altering propagation paths and highlighting the significant effect of void size and distribution on the fracture process. This systematic experimental evaluation provided critical insights into how microscale structural variations control fracture mechanics, laying a robust foundation for future theoretical and computational studies aimed at optimizing mechanical integrity and durability of functionally graded microcellular structures. Finally, Section 2.4 addressed dynamic fracture propagation, an essential aspect given the frequent exposure of engineering structures to dynamic and impact loads. Leveraging the homogenization framework previously established, the current research extended peridynamic modeling through the innovative application of Timoshenko beam theory, capturing shear and rotational dynamics typically neglected in traditional bond-based peridynamics. This novel computational model facilitated accurate simulation of dynamic mixed-mode fracture phenomena in microcellular materials, effectively capturing complex crack propagation paths influenced by both material and void-induced anisotropy. Such predictive capabilities are critical for designing resilient, impact-resistant microcellular structures across various demanding applications. Throughout this doctoral journey, our research consistently emphasized bridging theoretical advancements with practical, empirical validation. Each component of the current dissertation significantly contributes to the broader fracture mechanics discipline, addressing both longstanding theoretical limitations and contemporary material challenges. By developing robust computational tools, innovative fracture criteria, and extensive experimental datasets, this research equips engineers and material scientists with comprehensive resources to accurately predict fracture phenomena and optimize material performance. The insights and methodologies developed herein provide a foundation for future research, inspiring ongoing innovation and improved reliability across advanced materials engineering and structural design disciplines.
Recommended Citation
Shahbazian, Behnam, "Mixed-Mode Fracture Analysis of Additively Manufactured Periodic Orthotropic Functionally Graded Microcellular Materials" (2025). Theses and Dissertations. 1555.
https://repository.fit.edu/etd/1555
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