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Structural adhesives are widely used with great success, and yet occasional failures can occur, often resulting from improper bonding procedures or joint design, overload or other detrimental service situations, or in response to a variety of environmental challenges. In these situations, cracks can start within the adhesive layer or debonds can initiate near an interface. The paths taken by propagating cracks can affect the resistance to failure and the subsequent service lives of the bonded structures. The behavior of propagating cracks in adhesive joints remains of interest, including when some critical environments, complicated loading modes, or uncertainties in material/interfacial properties are involved. From a mechanics perspective, areas of current interest include understanding the growth of damage and cracks, loading rate dependency of crack propagation, and the effect of mixed mode fracture loading scenarios on crack path selection. This dissertation involves analytical, numerical, and experimental evaluations of crack propagation in several adhesive joint configurations. The main objective is an investigation of crack path selection in adhesively bonded joints, focusing on in-plane fracture behavior (mode I, mode II, and their combination) of bonded joints with uniform bonding, and those with locally weakened interfaces. When removing cured components from molds, interfacial debonds can sometimes initiate and propagate along both mold surfaces, resulting in the molded product partially bridging between the two molds and potentially being damaged or torn. Debonds from both adherends can sometimes occur in weak adhesive bonds as well, potentially altering the apparent fracture behavior. To avoid or control these multiple interfacial debonding, more understanding of these processes is required. An analytical model of 2D parallel bridging was developed and the interactions of interfacial debonds were investigated using Euler-Bernoulli beam theory. The numerical solutions to the analytical results described the propagation processes with multiple debonds, and demonstrated some common phenomena in several different joints corresponding to double cantilever beam configurations. The analytical approach and results obtained could prove useful in extensions to understanding and controlling debonding in such situations and optimization of loading scenarios. Numerical capabilities for predicting crack propagation, confirmed by experimental results, were initially evaluated for crack behavior in monolithic materials, which is also of interest in engineering design. Several test cases were devised for modified forms of monolithic compact tension specimens (CT) were developed. An asymmetric variant of the CT configuration, in which the initial crack was shifted to two thirds of the total height, was tested experimentally and numerically simulated in ABAQUS®, with good agreement. Similar studies of elongated CT specimens with different specimen lengths also revealed good agreement, using the same material properties and cohesive zone model (CZM) parameters. The critical specimen length when the crack propagation pattern abruptly switches was experimentally measured and accurately predicted, building confidence in the subsequent studies where the numerical method was applied to bonded joints. In adhesively bonded joints, crack propagation and joint failure can potentially result from or involve interactions of a growing crack with a partially weakened interface, so numerical simulations were initiated to investigate such scenarios using ABAQUS®. Two different cohesive zone models (CZMs) are applied in these simulations: cohesive elements for strong and weak interfaces, and the extended finite element method (XFEM) for cracks propagating within the adhesive layer. When the main crack approaches a locally weakened interface, interfacial damage can occur, allowing for additional interfacial compliance and inducing shear stresses within the adhesive layer that direct the growing crack toward the weak interface. The maximum traction of the interfacial CZM appears to be the controlling parameter. Fracture energy of the weakened interface is shown to be of secondary importance, though can affect the results when particularly small (e.g. 1% that of the bulk adhesive). The length of the weakened interface also has some influence on the crack path. Under globally mixed mode loadings, the competition between the loading and the weakened interface affects the shear stress distribution and thus changes the crack path. Mixed mode loading in the opposite direction of the weakened interface is able to drive the crack away from the weakened interface, suggesting potential means to avoid failure within these regions or to design joints that fail in a particular manner. In addition to the analytical and numerical studies of crack path selection in adhesively bonded joints, experimental investigations are also performed. A dual actuator load frame (DALF) is used to test beam-like bonded joints in various mode mixity angles. Constant mode mixity angle tracking, as well as other versatile loading functions, are developed in LabVIEW® for use with a new controller system. The DALF is calibrated to minimize errors when calculating the compliance of beam-like bonded joints. After the corrections, the resulting fracture energies ( ) values are considered to be more accurate in representing the energy released in the crack propagation processes. Double cantilever beam (DCB) bonded joints consisting of 6061-T6 aluminum adherends bonded with commercial epoxy adhesives (J-B Weld, or LORD 320/322) are tested on the DALF. Profiles of the values for different constant mode mixity angles, as well as for continuously increasing mode mixity angle, are plotted to illustrate the behavior of the crack in these bonded joints. Finally, crack path selection in DCB specimens with one of the bonding surfaces weakened was studied experimentally, and rate-dependency of the crack path selection was found. Several contamination schemes are attempted, involving of graphite flakes, silicone tapes, or silane treatments on the aluminum oxide interfaces. In all these cases, tests involving more rapid crack propagation resulted in interfacial failures at the weakened areas, while slower tests showed cohesive failure throughout. One possible explanation of this phenomenon is presented using the rate-dependency of the yield stress (commonly considered to be corresponding to the maximum traction) of the epoxy adhesives. These experimental observations may have some potential applications tailoring adhesive joint configurations and interface variability to achieve or avoid particular failure modes. / Ph. D.

In der vorliegenden Arbeit wird die Frage untersucht, ob effektive Eigenschaften von Verbunden auch nach dem Auftreten einer Dehnungslokalisierung aufgrund von entfestigendem Materialverhalten noch durch numerische Homogenisierungsmethoden berechnet werden können. Ihr Nutzen für diesen Anwendungsfall wird in der Literatur kritisch beurteilt. Aus diesem Grund werden hier systematisch alle Teilaufgaben betrachtet, die zu diesem Zweck gelöst werden müssen. Die erste dieser Aufgaben ist die Charakterisierung der einzelnen Verbundbestandteile. Zur Demonstration einer experimentell gestützten Charakterisierung wird ein glasfaserverstärktes Epoxidharz als Beispielmaterial gewählt. Neben der Beschreibung von Faser- und Matrixmaterial wird besonderes Augenmerk auf die Charakterisierung der Grenzschicht zwischen beiden gelegt. Die für die Glasfasern vorliegenden Festigkeitsmessungen entsprechen nicht der Kettenhypothese. Daher werden zahlreiche Verallgemeinerungen der Weibull-Verteilung untersucht, um störende Effekte zu erfassen. Schließlich werden Wahrscheinlichkeitsverteilungen hergeleitet, die Faserbrüche im Bereich der Einspannung einbeziehen. Die Messwerte können von diesen Verteilungen gut wiedergegeben werden. Zusätzlich macht ihre Anwendung das aufwändige Aussortieren und Wiederholen jener Experimente unnötig, bei denen der Faserbruch im Klemmbereich auftritt. Zur Modellierung der Grenzfläche wird ein Kohäsivzonengesetz entwickelt. Die Bestimmung seiner Parameter erfolgt anhand von Daten aus Pullout- und Einzelfaserfragmentierungsversuchen. Aus diesen ermittelte Festigkeiten und Energiefreisetzungsraten weisen eine sehr gute Übereinstimmung zwischen beiden Versuchen auf. Dabei erfolgt die Parameteridentifikation mithilfe von Finite-Elemente-Modellen anstatt der häufig genutzten vereinfachten analytischen Modelle, welche üblicherweise eine schlechtere Übereinstimmung erreichen. Sobald eine Dehnungslokalisierung auftritt, ist neben der Materialmodellierung auch das Homogenisierungsschema zu verallgemeinern. Zu diesem gehören die Generierung repräsentativer Volumenelemente, Randbedingungen (RB) und ein Mittelungsoperator. Anhand des aktuellen Standes der Literatur werden die Randbedingungen als ein signifikanter Schwachpunkt von Homogenisierungsverfahren erkannt. Daher erfolgt die Untersuchung periodischer RB, linearer Verschiebungsrandbedingungen und minimal kinematischer RB sowie zweier adaptiver RB, nämlich Lokalisierungspfad-ausgerichteter RB und generalisiert periodischer RB. Unter der Bezeichnung Tesselationsrandbedingungen wird ein weiterer Typ adaptiver RB vorgeschlagen. Zunächst erfolgt der Beweis, dass alle drei adaptiven RB die Hill-Mandel-Bedingung erfüllen. Des Weiteren wird mittels einer Modifikation der Hough-Transformation ein systematischer Fehler derselben bei der Bestimmung der Richtung von Lokalisierungszonen eliminiert. Schließlich werden die Eigenschaften aller Randbedingungen an verschiedenen Beispielen demonstriert. Dabei zeigt sich, dass nur Tesselationsrandbedingungen sowohl beliebige Richtungen von Lokalisierungszonen erlauben als auch fehlerhafte Lokalisierungen in Eckbereichen ausschließen. Zusammengefasst können in der Literatur geäußerte grundlegende Einschränkungen hinsichtlich der Anwendbarkeit numerischer Homogenisierungsverfahren beim Auftreten von Dehnungslokalisierungen aufgehoben werden. Homogenisierungsmethoden sind somit auch für entfestigendes Materialverhalten anwendbar. / The thesis at hand is concerned with the question if numerical homogenization schemes can be of use in deriving effective material properties of composite materials after the onset of strain localization due to strain softening. In this case, the usefulness of computational homogenization methods has been questioned in the literature. Hence, all the subtasks to be solved in order to provide a successful homogenization scheme are investigated herein. The first of those tasks is the characterization of the constituents, which form the composite. To allow for an experimentally based characterization an exemplary composite has to be chosen, which herein is a glass fiber reinforced epoxy. Hence the constituents to be characterized are the epoxy and the glass fibers. Furthermore, special attention is paid to the characterization of the interface between both materials. In case of the glass fibers, the measured strength values do not comply with the weakest link hypothesis. Numerous generalizations of the Weibull distribution are investigated, to account for interfering effects. Finally, distributions are derived, that incorporate the possibility of failure inside the clamped fiber length. Application of such a distribution may represent the measured data quite well. Additionally, it renders the cumbersome process of sorting out and repeating those tests unnecessary, where the fiber fails inside the clamps. Identifying the interface parameters of the proposed cohesive zone model relies on data from pullout and single fiber fragmentation tests. The agreement of both experiments in terms of interface strength and energy release rate is very good, where the parameters are identified by means of an evaluation based on finite element models. Also, the agreement achieved is much better than the one typically reached by an evaluation based on simplified analytical models. Beside the derivation of parameterized material models as an input, the homogenization scheme itself needs to be generalized after the onset of strain localization. In an assessment of the current state of the literature, prior to the generation of representative volume elements and the averaging operator, the boundary conditions (BC) are identified as a significant issue of such a homogenization scheme. Hence, periodic BC, linear displacement BC and minimal kinematic BC as well as two adaptive BC, namely percolation path aligned BC and generalized periodic BC are investigated. Furthermore, a third type of adaptive BC is proposed, which is called tesselation BC. Firstly, the three adaptive BC are proven to fulfill the Hill-Mandel condition. Secondly, by modifying the Hough transformation an unbiased criterion to determine the direction of the localization zone is given, which is necessary for adaptive BC. Thirdly, the properties of all the BC are demonstrated in several examples. These show that tesselation BC are the only type, that allows for arbitrary directions of localization zones, yet is totally unsusceptible to spurious localization zones in corners of representative volume elements. Altogether, fundamental objections, that have been raised in the literature against the application of homogenization in situations with strain localization, are rebutted in this thesis. Hence, the basic feasibility of homogenization schemes even in case of strain softening material behavior is shown.

With continued feature size reduction in microelectronics and with more than a billion transistors on a single integrated circuit (IC), on-chip interconnection has become a challenge in terms of processing-, electrical-, thermal-, and mechanical perspective. Today’s high-performance ICs have on-chip back-end-of-line (BEOL) layers that consist of copper traces and vias interspersed with low-k dielectric materials. These layers have thicknesses in the range of 100 nm near the transistors and 1000 nm away from the transistors close to the solder bumps. In such BEOL layered stacks, cracking and/or delamination is a common failure mode due to the low mechanical and adhesive strength of the dielectric materials as well as due to high thermally-induced stresses. However, there are no available cohesive zone models and parameters to study such interfacial cracks in sub-micron thick microelectronic layers. This work focuses on developing framework based on cohesive zone modeling approach to study interfacial delamination in sub-micron thick layers. Such a framework is then successfully applied to predict microelectronic device reliability. As intentionally creating pre-fabricated cracks in such interfaces is difficult, this work examines a combination of four-point bend and double-cantilever beam tests to create initial cracks and to develop cohesive zone parameters over a range of mode-mixity. Similarly, a combination of four-point bend and end-notch flexure tests is used to cover additional range of mode-mixity. In these tests, silicon wafers obtained from wafer foundry are used for experimental characterization. The developed parameters are then used in actual microelectronic device to predict the onset and propagation of crack, and the results from such predictions are successfully validated with experimental data. In addition, nanoindenter-based shear test technique designed specifically for this study is demonstrated. The new test technique can address different mode mixities compared to the other interfacial fracture characterization tests, is sensitive to capture the change in fracture parameter due to changes in local trace pattern variations around the vicinity of bump and the test mimics the forces experienced by the bump during flip-chip assembly reflow process. Through this experimental and theoretical modeling research, guidelines are also developed for the reliable design of BEOL stacks for current and next-generation microelectronic devices.

Carbon Fiber / Epoxy Laminates are increasingly being used in the primary structure of aircraft. To make effective use these materials, it is necessary to consider the ability of a laminate to resist damage, as well as material strength and stiffness. A possible means for improving damage tolerance is the use of non-traditional composite laminates, in which the longitudinal 0 plies are replaced with 5 or 10 plies. The main objectives of this collaborative Georgia Tech / Boeing research was the characterization of these non-traditional laminates, and the determination of appropriate lamina-level analytical techniques that are capable of predicting the changes caused by the use of slightly off-axis longitudinal plies. A quasi-isotropic [45/90/-45/theta/45/90/-45/-theta]s and hard [45/theta/-45/theta/90/45]s lay-up, where theta =0,5 or 10, were tested in open hole tension, filled hole tension, open hole compression, single shear bearing, and unnotched tension. These coupon level tests illustrated the effects of lay-up, notch constraint, and load type on traditional and non-traditional laminates. Die penetrant enhanced in-situ radiography was performed to determine the extent of damage suppression. The use of non-traditional laminates was found to reduce longitudinal ply cracking and delamination, with significant effect on the stress distribution around the notch. The use of non-traditional laminates also resulted in a 15%-20% improvement in bearing strength of the traditional laminates. Several predictive techniques were implemented to evaluate their ability to predict the effect of slight changes in ply orientations. A progressive damage model was written to compare Tsai-Wu, Hashin, and Maximum Stress unnotched strength criterion. Additionally, several semi-empirical failure theories for notched strength prediction were compared with linear and bi-linear cohesive zone models to determine applicability to non-traditional laminates.

<p dir="ltr">In structural metallic components, a material’s lifecycle begins with the processing route, to produce a desired structure, which dictates the in-service performance. The variability of microstructural features as a consequence of the processing route has a direct influence on the properties and performance of a material. In order to correlate the influence processing conditions have on material performance, large test matrices are required which tend to be time consuming and expensive. An alternative route to avoid such large test matrices is to incorporate physics-based process modeling and lifing paradigms to better understand the performance of structural materials. By linking microstructural information to the material’s lifecycle, the processing path can be modified without the need to repeat large-scale testing requirements. Additionally, when a materials system is accurately modeled throughout its lifecycle, the performance predictions can be leveraged to improve the design of materials and components.</p><p dir="ltr">Ni-based superalloys are a material class widely used in many critical aerospace components exposed to coupling thermal and mechanical loads due to their increased resistance to creep, corrosion, oxidation, and strength characteristics at elevated temperatures. Many Ni-based superalloys undergo high-temperature forging to produce a desired microstructure, targeting specific strength and fatigue properties in order to perform under thermo-mechanical loads. When in-service, these alloys tend to fail as a consequence of thermo-mechanical fatigue (TMF) from either inclusion- or matrix- driven failure. In order to produce safer, cheaper and more efficient critical aerospace components, the micromechanical deformation and damage mechanisms throughout a Ni-based superalloy’s lifecycle must be understood. This research utilizes process modeling as a tool to understand the damage and deformation of inclusions in a Ni-200 matrix throughout radial forging as a means to optimize the processing conditions for improved fatigue performance. In addition, microstructural sensitive performance modeling for a Ni-based superalloy is leveraged to understand the influence TMF has on damage mechanisms.</p><p dir="ltr">The radial forging processing route requires both high temperatures and large plastic deformation. During this process, non-metallic inclusions (NMIs) can debond from the metallic matrix and break apart, resulting in a linear array of smaller inclusions, known as stringers. The evolution of NMIs into stringers can result in matrix load shedding, localized plasticity, and stress concentrations near the matrix-NMI interface. Due to these factors, stringers can be detrimental to the fatigue life of the final forged component. By performing a finite element model of the forging process with cohesive zones to simulate material debonding, this research contributes to the understanding of processing induced deformation and damage sequences on the onset of stringer formation for Alumina NMIs in a Ni-200 matrix. Through a parametric study, the interactions of forging temperature, strain rate, strain per pass, and interfacial decohesion on the NMI damage evolution metrics are studied, specifically NMI particle separation, rotation, and cavity formation. The parametric study provides a linkage between the various processing conditions parameters influence on detrimental NMI morphology related to material performance.</p><p dir="ltr">The microstructural characteristics of Ni-based superalloys, as a consequence of a particular processing route, creates a variability in TMF performance. The micromechanical failure mechanisms associated with TMF are dependent on various loading parameters, such as temperature, strain range, and strain-temperature phasing. Insights on the complexities of micromechanical TMF damage are studied via a temperature-dependent, dislocation density-based crystal plasticity finite element (CPFE) model with uncertainty quantification. The capabilities of the model’s temperature dependency are examined via direct instantiation and comparison to a high-energy X-ray diffraction microscopy (HEDM) experiment under coupled thermal and mechanical loads. Unique loading states throughout the experiment are investigated with both CPFE predictions and HEDM results to study early indicators of TMF damage mechanisms at the grain scale. The mesoscale validation of the CPFE model to HEDM experimental data provides capabilities for a well-informed TMF performance paradigm under various strain-temperature phase profiles. </p><p dir="ltr">A material’s TMF performance is highly dependent on the temperature-load phase profile as a consequence of path-dependent thermo-mechanical plasticity. To investigate the relationship between microstructural damage and TMF phasing effects, the aforementioned CPFE model investigates in-phase (IP) TMF, out-of-phase (OP) TMF, and iso-thermal (ISO) loading profiles. A microstructural sensitive performance modeling framework with capabilities to isolate phasing (IP, OP, and ISO) effects is presented to locate fatigue damage in a set of statistically equivalent microstructures (SEMs). Location specific plasticity, and grain interactions are studied under the various phasing profiles providing a connection between microstructural material damage and TMF performance.</p>

Global-local finite element analyses were used to study the damage tolerance of curvilinearly stiffened panels; fabricated using the modern additive manufacturing process, the so-called unitized structures, and that of adhesive joints. A damage tolerance study of the unitized structures requires cracks to be defined in the vicinity of the critical stress zone. With the damage tolerance study of unitized structures as the focus, responses of curvilinearly stiffened panels to the combined shear and compression loadings were studied for different stiffeners' height. It was observed that the magnitude of the minimum principal stress in the panel was larger than the magnitudes of the maximum principal and von Mises stresses. It was also observed that the critical buckling load factor increased significantly with the increase of stiffeners' height. To study the damage tolerance of curvilinearly stiffened panels, in the first step, buckling analysis of panels was performed to determine whether panels satisfied the buckling constraint. In the second step, stress distributions of the panel were analyzed to determine the location of the critical stress under the combined shear and compression loadings. Then, the fracture analysis of the curvilinearly stiffened panel with a crack of size 1.45 mm defined at the location of the critical stress, which was the common location with the maximum magnitude of the principal stresses and von Mises stress, was performed under combined shear and tensile loadings. This crack size was used because of the requirement of a sufficiently small crack, if the crack is in the vicinity of any stress raiser. A mesh sensitivity analysis was performed to validate the choice of the mesh density near the crack tip. All analyses were performed using global-local finite element method using MSC. Marc, and global finite element methods using MSC. Marc and ABAQUS. Negligible difference in results and 94% saving in the CPU time was achieved using the global-local finite element method over the global finite element method by using a mesh density of 8.4 element/mm ahead of the crack tip. To study the influence of different loads on basic modes of fracture, the shear and normal (tensile) loads were varied differently. It was observed that the case with the fixed shear load but variable normal loads and the case with the fixed normal load but variable shear loads were Mode-I. Under the maximum combined loading condition, the largest effective stress intensity factor was very smaller than the critical stress intensity factor. Therefore, considering the critical stress intensity factor of the panel with the crack of size 1.45 mm, the design of the stiffened panel was an optimum design satisfying damage tolerance constraints. To acquire the trends in stress intensity factors for different crack lengths under different loadings, fracture analyses of curvilinearly stiffened panels with different crack lengths were performed by using a global-local finite element method under three different load cases: a) a shear load, b) a normal load, and c) a combined shear and normal loads. It was observed that 85% data storage space and the same amount in CPU time requirement could be saved using global-local finite element method compared to the standard global finite element analysis. It was also observed that the fracture mode in panels with different crack lengths was essentially Mode-I under the normal load case; Mode-II under the shear load case; and again Mode-I under the combined load case. Under the combined loading condition, the largest effective stress intensity factor of the panel with a crack of recommended size, if the crack is not in the vicinity of any stress raiser, was very smaller than the critical stress intensity factor. This work also includes the performance evaluation of adhesive joints of two different materials. This research was motivated by our experience of an adhesive joint failure on a test-fixture that we used to experimentally validate the design of stiffened panels under a compression-shear load. In the test-fixture, steel tabs were adhesively bonded to an aluminum panel and this adhesive joint debonded before design loads on the test panel were fully applied. Therefore, the requirement of studying behavior of adhesive joints for assembling dissimilar materials was found to be necessary. To determine the failure load responsible for debonding of adhesive joints of two dissimilar materials, stress distributions in adhesive joints of the nonlinear finite element model of the test-fixture were studied under a gradually increasing compression-shear load. Since the design of the combined load test fixture was for transferring the in-plane shear and compression loads to the panel, in-plane loads might have been responsible for the debonding of the steel tabs, which was similar to the results obtained from the nonlinear finite element analysis of the combined load test fixture. Then, fundamental studies were performed on the three-dimensional finite element models of adhesive lap joints and the Asymmetric Double Cantilever Beam (ADCB) joints for shear and peel deformations subjected to a loading similar to the in-plane loading conditions in the test-fixtures. The analysis was performed using ABAQUS, and the cohesive zone modeling was used to study the debonding growth. It was observed that the stronger adhesive joints could be obtained using the tougher adhesive and thicker adherends. The effect of end constraints on the fracture resistance of the ADCB specimen under compression was also investigated. The numerical observations showed that the delamination for the fixed end ADCB joints was more gradual than for the free end ADCB joints. Finally, both the crack propagation and the characteristics of adhesive joints were studied using a global-local finite element method. Three cases were studied using the proposed global-local finite element method: a) adhesively bonded Double Cantilever Beam (DCB), b) an adhesive lap joint, and c) a three-point bending test specimen. Using global-local methods, in a crack propagation problem of an adhesively bonded DCB, more than 80% data storage space and more than 65% CPU time requirement could be saved. In the adhesive lap joints, around 70% data storage space and 70% CPU time requirement could be saved using the global-local method. For the three-point bending test specimen case, more than 90% for both data storage space and CPU time requirement could be saved using the global-local method. / Ph. D.