Adhesive bonding which has been in use for long as a traditional joining method has gained ground in the last couple of decades due to the introduction of advanced composite materials into the aerospace industry. Bonded structures have advantages such as high corrosion and fatigue resistance, ability to join dissimilar materials, reduced stress concentration, uniform stress distribution, good damping characteristics etc. They also have certain limitations like environmental degradation, existence of defects like pores, voids and disbonds, difficulty in maintenance and repair etc. A serious drawback in the use of adhesively bonded structures has been that there are no established comprehensive non-destructive testing (NDT) techniques for their evaluation. Further, a reliable evaluation of the effect of the existing defects on strength and durability of adhesive joints is yet to be achieved. This has been a challenge for the research and development community over several decades and hence, been the motivation behind this piece of research work. Under the scope of the work carried out in the thesis, some of the primary factors such as the existence of defects, degradation of the adhesive, stress and strain distribution in the bonded region etc., have been considered to study the bond integrity in composite to composite lap shear joints. The problem becomes complex if all the parameters affecting the adhesive joint are varied simultaneously. Taking this into consideration, one of the key parameters affecting the bond quality, viz., the adhesive layer degradation was chosen to study its effect on the bonded joint. The epoxy layer was added with different, definite amount of Poly vinyl alcohol (PVA) to arrive at sets of bonded joint specimens with varied adhesive layer properties. A thorough review of different non destructive testing methods applied to this particular problem showed that ultrasonic wave based techniques could be the right choice. To start with, preliminary experimental investigations were carried on unidirectional glass fiber reinforced plastic (GFRP-epoxy) lap joints. The adhesive joints were subjected to non destructive evaluation (NDE) using ultrasonic through transmission and pulse echo techniques as also low energy digital X-ray techniques. The results obtained showed a variation in reflected and transmitted ultrasonic pulse amplitude with bond quality. Digital X-Ray radiography technique showed a variation in the intensity of transmitted x-rays due to variation in the density of adhesive. Standard mechanical tests revealed that the addition of PVA decreased the bond strength. A plot of coefficient of reflection from the first interface and the bond strength showed a linear correlation between them. After obtaining a cursory feel and understanding of the parameters involved with the preliminary experiments on GFRP adhesive joints which yielded interesting and encouraging results, further work was carried on specimens made out of autoclave cured carbon fiber reinforced plastic (CFRP)-epoxy bonded joints. Normal incidence ultrasound showed a similar trend. Analyses of the Acoustic Emission (AE) signals generated indicate early AE activity for degraded joints compared to healthy joints. Literary evidences suggest that the ultrasonic shear waves are more sensitive to interfacial degradation. An attempt was made to use oblique incidence ultrasonic interrogation using shear waves. The amplitude of reflected shear waves from the interface increased with an increase in degradation. Further, a signal analysis approach in the frequency domain revealed a shift in the frequency minimum towards lower range in degraded samples. This phenomenon was verified using analytical models. An inversion algorithm was used to determine the interfacial transverse stiffness which decreased significantly due to increase in degradation. Conventional ultrasonic evaluation methods are rendered ineffective when a direct access to the test region is not possible; a different approach with guided wave techniques can be explored in this scenario. Investigations on CFRP-epoxy adhesive joints using Lamb waves showed a decrease in the amplitude of ‘So’ mode in degraded samples. Theoretical dispersion curves exhibited a similar trend. Frequency domain studies on the received modes using Gabor wavelet transform showed a negative shift in frequency with increased degradation. It was also observed that the maximum transmission loss for the most degraded sample with 40 percent PVA occurred in the range of 650 – 800 kHz. Non linear ultrasonic (NLU) evaluation revealed that the nonlinearity parameter (β) increased with increased degradation. Kissing bonds are most commonly occurring type of defects in adhesive joints and are very difficult to characterize. A recent non-contact imaging technique called digital image correlation (DIC) was tried to evaluate composite adhesive joints with varied percentage of inserted kissing bond defects. The results obtained indicate that DIC can detect the kissing bonds even at 50 percent of the failure load. In addition, to different experimental approaches to evaluate the bonded joint discussed above, the effect of degradation on the stresses in the bond line region was studied using analytical and numerical approach. A linear adhesive beam model based on Euler beam theory and a nonlinear adhesive beam model based on Timoshenko beam theory were used to determine the adhesive peel and shear stress in the joint. Digital image correlation technique was used to experimentally obtain the bond line strains and corresponding stresses were computed assuming a plane strain condition. It was found that the experimental stresses followed a similar trend to that predicted by the two analytical models. A maximum peel stress failure criterion was used to predict failure loads. A failure mechanism was proposed based on the observations made during the experimental work. It was further shown that the critical strain energy release rate for crack initiation in a healthy joint is much higher compared to a degraded joint. The analytical models become cumbersome if a larger number of factors have to be taken into account. Numerical methods like finite element analysis are found to be promising in overcoming these hurdles. Numerical investigation using 3D finite element analysis was carried out on CFRP-epoxy adhesive joints. The adherend – adhesive interface was modeled using connector elements whose stiffness properties as well as the bulk adhesive properties for joints with different amounts of PVA were determined using ultrasonic inspection method. The peel and shear stress variation along the adhesive bond line showed a similar trend as observed with the experimental stress distribution (DIC) but with a lesser magnitude. A parametric study using finite element based Monte-Carlo simulation was carried out to assess the effect of variation in various joint parameters like adhesive modulus, bondline thickness, adherend geometrical and material properties on peel and shear stress in the joint. It was found that the adhesive modulus and bond line thickness had a significant influence on the magnitude of stresses developed in the bond line. Thus, to summarize, an attempt has been made to study the bond line integrity of a composite epoxy adhesive lap joint using experimental, analytical and numerical approaches. Advanced NDE tools like oblique incidence ultrasound, non linear ultrasound, Lamb wave inspection and digital image correlation have been used to extract parameters which can be used to evaluate composite bonded joints. The results obtained and reported in the thesis have been encouraging and indicate that in specific cases where the bond line thickness and other relevant parameters if can be maintained or presumed reasonably non variant, it is possible to effectively evaluate the integrity of a composite bonded joint.

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.