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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.