The interface crack branching phenomena, including thermal effects, has been investigated by using complex variable method and Stroh's dislocation theory, extended to thermo-elasticity in matrix notation. As one of the most catastrophic failure modes in structures like laminated and sandwich composites in aerospace and marine construction, thin film in electronic packaging, rotators in high speed engine of aircraft and reactor in nuclear power station, the study of interface crack branching has become a topic not only having theoretical importance, but also having practical significance. A unified approach is presented to address the thermoelastic interface crack problems in dissimilar anisotropic bimaterial composites, and a compact closed form solution is formulated by analytical continuation principle of complex analysis. Employing the contour integral method, an explicit solution to the interaction between the dislocations and the interface crack is obtained. By modeling the branched portion as a continuous distribution of the dislocations, the thermoelastic interface crack branching problem is then converted to a set of semi-coupled singular integral equations and solved by Gauss-Jacobi integration schemes. The influence of material property mismatches between the two constituents and the thermal loading effects on the interface crack branching are demonstrated by extensive numerical simulation. Some useful criteria for predicting the interface crack branching growth and guidance for optimal composites design are suggested. Further, a contact model to eliminate the overlapping between the two surfaces of an interface crack is also proposed and some new parameters which could influence the interpenetrating phenomena are also discovered. The technique to extend the current method to three dimensional problems is also outlined. Furthermore, the C++ source code has been implemented to manipulate the complicated complex operations for numerically solving the singular integral equations in complex matrix form.

In today&#039 / s technology severe working conditions increase demands on structural materials. A class of materials which are developed to meet these increased demands is Functionally Graded Materials (FGMs). These are inhomogeneous structural materials which are able to withstand large temperature gradients and corrosive environment. Application areas of FGMs are in aerospace industry, nuclear reactors, chemical plants and turbine systems. FGMs have gradual compositional variation from metal to ceramic which give them mechanical strength, toughness and heat resistance. However under high temperature gradients, cracking problems may arise due to thermal stresses. In layered structures the final stage of failure may be delamination due to crack extension. The objective of this study is to model a particular type of crack problem in a layered structure consisting of a substrate, a bond coat and an orthotropic FGM coating. There is an internal crack in the orthotropic layer and it is perpendicular to material gradation of coating. The position of the crack inside the coating is kept as a variable. The steady-state temperature distribution between the substrate and the coating causes a buckled shape along crack face. The critical temperature change, temperature distribution, mixed mode stress intensity values and energy release rates are calculated by using Displacement Correlation Technique. Results of this study present the effects of geometric parameters such as crack length, crack position, etc as well as the effects of the type of gradation on buckling behavior and mixed mode stress intensity factors.

The two-dimensional interface crack problem is investigated for anisotropic bodies in the Comninou formulation. It is established that, as in the isotropic case, properly incorporating contact zones at the crack tips avoids contradictions connected with the oscillating asymptotic behaviour of physical and mechanical characteristics leading to the overlapping of material. Applying the special integral representation formulae for the displacement field the problem in question is reduced to the scalar singular integral equation with the index equal to -1. The analysis of this equation is given. The comparison with the results of previous authors shows that the integral equations corresponding to the interface crack problems in the anisotropic and isotropic cases are actually the same from the point of view of the theoretical and numerical analysis.

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The two-dimensional interface crack problem is investigated for anisotropic bodies in the Comninou formulation. It is established that, as in the isotropic case, properly incorporating contact zones at the crack tips avoids contradictions connected with the oscillating asymptotic behaviour of physical and mechanical characteristics leading to the overlapping of material. Applying the special integral representation formulae for the displacement field the problem in question is reduced to the scalar singular integral equation with the index equal to -1. The analysis of this equation is given. The comparison with the results of previous authors shows that the integral equations corresponding to the interface crack problems in the anisotropic and isotropic cases are actually the same from the point of view of the theoretical and numerical analysis.

This Ph.D. thesis deals with modeling of compound structures containing defects such as cracks or notches. Attention was mainly focused on structures manufactured out of metals and polymers. Presented results were obtained from experimental measurements, which were compared with theoretical estimations of the ultimate states of the compound structures. Theoretical estimations were obtained by the application of the generalized fracture mechanics, whose integral part is based on numerical solution provided by finite element method. The results of the Ph.D. thesis contribute both to prediction of the limit states of compound objects, and to verification of the validity of the generalized fracture mechanics.

This thesis presents the development of a new multiscale stochastic fracture mechanics modelling framework informed by in-situ X-ray Computed Tomography (X-ray CT) tests, which can be used to enhance the quality of new designs and prognosis practices for fibre reinforced composites. To reduce the empiricism and conservatism of existing methods, this PhD research systematically has tackled several challenging tasks including: (i) extension of the cohesive interface crack model to multi-phase composites in both 2D and 3D, (ii) development of a new in-house loading rig to support in-situ X-ray CT tests, (iii) reconstruction of low phase-contrast X-ray CT datasets of carbon fibre composites, (iv) integration of X-ray CT image-based models into detailed crack propagation FE modelling and (v) validation of a partially informed multiscale stochastic modelling method by direct comparison with in-situ X-ray CT tensile test results.

Es werden hydrostatisch stranggepresste Aluminium/Magnesium-Verbunde untersucht. Mittels verschiedener Rissdetektionsmethoden wird die Beschaffenheit des Interface analysiert. Es erfolgt die Bestimmung von Fließkurven der verpressten Einzelwerkstoffe bei Raumtemperatur. Des Weiteren erfolgen Eigenspannungsanalysen mit dem Bohrlochverfahren und einer speziellen numerischen Auswertungsmethode, welche den Entstehungsprozess der Eigenspannungen berücksichtigt. Zur Analyse der Festigkeitseigenschaften und des Deformationsverhaltens des Interface werden Biegeversuche in einem erweiterten Temperaturbereich durchgeführt. Die Deformationsanalyse erfolgt mittels Digital Image Correlation. Des Weiteren finden in den Festigkeitsuntersuchungen Push-Out-Versuche Anwendung. In bruchmechanischen Analysen wird die Interfacerissspitze von speziell entwickelten Proben unter Mode I-Bedingungen, bezogen auf den homogenen Fall, beansprucht. Die bruchmechanischen Größen – kritischer betragsmäßiger Spannungsintensitätsfaktor und kritische Energiefreisetzungsrate – werden auf Basis der Experimente, der numerischen Simulation der Rissspitzenbeanspruchung sowie der für die linear-elastische Bruchmechanik des Interfacerisses geltenden Nahfeldgleichungen berechnet. / Hydrostatic coextruded aluminum/magnesium compounds are analyzed. By means of different methods of crack detection, the quality of the interface is investigated. Plastic behavior of the basic materials at room temperature is determined. Furthermore, residual stress analyses are performed using the hole drilling method and a special numerical evaluation procedure, which considers the formation process of the residual stresses. The strength and deformation behavior of the interface are determined by means of bending tests in an extended temperature range. Digital Image Correlation is used to analyze the deformation. Furthermore, push out tests are performed to determine the interface strength. In the course of fracture mechanical analyses, the crack tip of specially developed specimens is stressed under Mode I conditions (relating to homogeneous material). The fracture mechanical values – critical absolute value of the stress intensity factor and critical energy release rate – are determined by the use of experiments, numerical analyses of the crack tip fields as well as the equations of the linear elastic near field equations of interface fracture mechanics.

Předkládaná dizertační práce se zabývá stanovením hlavních členů Williamsova asymptotického rozvoje popisujícího rovinné elektro-elastické pole v okolí piezoelektrických bi-materiálových vrubů a trhlin na rozhraní za použití rozšířeného Lechnického-Eshelbyho-Strohova formalismu v návaznosti na čistě anizotropní pružnost. Je ukázáno, že rozšířený Lechnického-Eshelbyho-Strohův formalismus představuje spolu s moderními programovacími koncepty v jazyku Python efektivní a také praktický nástroj pro lomovou analýzu piezoelektrických bi-materiálů. Teoretická část práce popisuje aspekty anizotropní pružnosti a její návaznost na piezoelektrické materiály. Základní rovnice zaměřené na speciální typy monoklinických materiálů, které umožňují oddělení rovinného a anti-rovinného problému, jsou vyjádřeny pomocí komplexních potenciálů. V praktické části práce je sestaven problém vlastního hodnot pro bi-materiálový vrub, na jehož základě jsou stanoveny exponenty singularity a pomocí dvoustavového -integrálu také zobecněné faktory intenzity napětí. Veškeré vztahy a numerické procedury jsou následně rozšířeny na problém piezoelektrických bi-materiálových vrubů a podrobně prozkoumány v uvedených příkladech. Zvláštní pozornost je věnována přechodu asymptotického řešení téměř zavřených vrubů a trhlin na rozhraní. Vliv směru polarizace na asymptotické řešení je také zkoumán. Přesnost stanovení zobecněných faktorů intenzity napětí je testována srovnáním asymptotického řešení a řešení získaného pomocí metody konečných prvků s velmi jemnou sítí konečných prvků. Na závěr je formalismus modifikován pro nepiezoelektrické materiály.