Desenvolvem-se a formulação do Método dos Elementos de Contorno e correspondente algoritmo (para implementação em microcomputador) para a análise de propagação de fraturas em domínios bidimensionais. São utilizados elementos lineares isoparamétricos, tanto para discretizar o contorno quanto para simular a fratura. Os elementos de fratura são descontínuos. A formulação é baseada em equações integrais de tensões e de deslocamentos, onde o termo que considera tensões iniciais concentradas na linha de fratura é formulado a partir da definição de dipolos. O critério adotado é o modelo de fratura coesiva. Os termos singulares e hiper-singulares da formulação são tratados analiticamente e os termos quase-singulares são calculados através de um esquema numérico baseado na utilização de sub-elementos. Os valores dos dipolos são estimados ponto a ponto. Ao longo das fraturas, o valor máximo da tensão normal de tração permite definir novos elementos. As tensões de cisalhamento são removidas para manter a direção principal durante o processo. / The Boundary Element Method formulation and corresponding algorithrn (for microcomputer implementation) are developed for crack growth analysis in two-dimensional domains. Linear isoparametric elements are used to discretize both boundary and crack path. Fracture elements are assumed to be discontinuous. The formulation is based on stress and displacement integral equations, where the term that takes into account initial stresses concentrated along fracture line is formulated from dipoles definition. The coesive fracture rnodel is the criterium adopted. Singular and hipersingular formulation terms are anallitically treated and quasi-singular terms are computed by a numerical scheme based on element subdivision. Dipole values are estirnated point by point. Along fractures, the maximum normal tensile strenght is used to define new elements. Shear stresses are also removed to maintain the principal direction during the process.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 156-163. / by Chun Woon Lau. / Ph.D.

Dynamic fracture of metals is a fascinating multiphysics-multiscale problem that often results in brittle and/or ductile fracture of structural components. Additionally, under high strain rates such as impact or blast loads, a failure phenomena known as shear banding may also occur, which is a common precursor to fracture. Both fracture and shear banding are instability processes leading to strong discontinuities and strain localization, respectively. Namely, shear bands are zones of highly localized plastic deformation, while brittle/ductile cracks are material discontinuities due to cleavage and/or void coalescence. Furthermore, while fracture events are mostly driven by triaxial tensile loading, shear bands are driven by shear heating caused by inelastic deformations and high temperature rise. In this work, fracture is modeled through a phase field formulation coupled to a set of equations that describe shear bands. While fracture is governed by a strong length scale that propagates at a fast time scale, shear bands are dominated by a weak length scale and propagate slower. These are two different failure modes with distinct spatial and temporal scales. This thesis is aimed at the development of analytical and numerical methods to determine the onset of both shear band localization and fracture. The main contribution of this thesis is the formulation of analytical criteria, based on the linear perturbation method, for the onset of fracture and shear band instabilities. We first propose a stability framework for shear bands that account for a non-constant Taylor Quinney coefficient. In addition, we apply the linear perturbation method to the phase field formulation of fracture to study the onset of unstable crack growth. The derivations lead to an analytical, energy based criterion for the phase field method in linear elastic and visco-plastic materials. The stability criterion not only recovers the critical stress value reported in the literature for simple elastic cases but also provides a criterion for visco-plastic materials with a general degradation function and fracture induced by cold-work. Finally, we analyze the physical stability of both failure modes and their interaction. The analysis provides insight into the dominant failure mode and can be used as a criterion for mesh refinement. Several numerical results with different geometries and a range of strain rate loadings demonstrate that the stability criterion predicts well the onset of failure instability in dynamic fracture applications. For the example problems considered, if a fracture instability precedes shear banding, a brittle-like failure mode is observed, while if a shear band instability is initiated significantly before fracture, a ductile-like failure mode is expected. In any case, fracture instability is stronger than a shear band instability and if initiated will dominate the response. Another contribution of this thesis is the development of numerical type stability methods based on the discretized model which can be employed within any finite element method. In this approach, a novel methodology to determine the onset of shear band localization is proposed, by casting the instability analysis as a generalized eigenvalue problem with a particular decomposition of the element Jacobian matrix. We show that this approach is attractive, as it is applicable to general rate dependent multidimensional cases and no special simplifying assumptions ought to be made. Furthermore, this technique is also applied to the fully coupled dynamic fracture problem and is shown to agree well with the analytical criteria. Finally, we propose an alternative for identifying the instability point following a generalized stability analysis concept. In this framework, a stability measure is obtained by computing the instantaneous growth rate of the vector tangent to the solution. Such an approach is more appropriate for non-orthogonal problems and is easier to generalize to difficult dynamic fracture problems.

La compréhension du comportement des matériaux minces sous différentes sollicitations est un enjeu en matière de sécurité. Les modèles de comportement mécanique et de rupture ont évolué pour prendre en compte l’état de contrainte et la vitesse de déformation qui peuvent avoir une influence majeure sur la réponse du matériau. L’identification de ces modèles passe par la caractérisation expérimentale du matériau. Les essais mécaniques représentent donc toujours une étape indispensable au développement des outils numériques. L’objectif de ces travaux est donc de contribuer à l’apport de techniques expérimentales de caractérisation des matériaux. L’ensemble des travaux est illustré par l’étude de deux matériaux : un alliage d’aluminium AA- 2024-T3 et un acier dual phase DP450. L’effet de la vitesse de déformation sur le comportement en traction équi-biaxiale, ainsi que la déformation à rupture en traction équi-biaxiale et en traction en déformation plane sont étudiés. Pour cela, le dépouillement de l’essai de gonflement hydraulique (bulge test) est amélioré et un nouveau dispositif est utilisé pour atteindre des vitesses de déformation intermédiaires de 100 s-1. L’essai de poinçonnement hémisphérique et un nouvel essai de poinçonnement pour la traction en déformation plane sont effectués jusqu’à des vitesses de déformation intermédiaires. L’effet du trajet de chargement sur la déformation à rupture est également étudié. Une méthode de traction uni-axiale sur éprouvettes de grandes dimensions est développée pour appliquer un premier chargement. Ensuite un second chargement en traction équi-biaxiale ou en traction en déformation plane est appliqué jusqu’à rupture. / The understanding of thin materials behavior under various stress state is a current issue for security matters. Constitutive models and failure models evolved to take into account stress state and strain rate effect on material behavior. Experimental characterization of materials is necessary to identify models. Mechanical tests are mandatory for the development of numerical tools. The aim of this thesis is the development of experimental techniques for material characterization. This work is performed on two materials, a AA-2024-T3 aluminum alloy and DP450 dual phase steel. Strain rate effect on the equi-biaxial tension behavior and the failure, and on the plane strain tension failure is studied. For this purpose, we improved the analysis of bulge test and a new device is proposed ion order to attain strain rates up to 100 s-1. Hemispheric punch test and a new punch test dedicated to plane strain tension are proposed at high strain rates. Effect of loading path on failure strain is also studied. A new device for uniaxial tension on large specimens is use to apply the first load, a second loading under equi-biaxial tension or plane strain tension is then applied up to failure.

The employment of composite materials in the aerospace industry has been gradually considered due to the fundamental lightweight and strength characteristics that these type of materials offer. The science material and technological progress that has been reached, matches perfectly with the requirements for high-performance materials in aircraft and aerospace structures, thus, the development of primary structure elements applying composite materials became something very convenient. It is extremely important to pay attention to the failure modes that influence composite materials performances, since, these failures lead to a loss of stiffness and strength of the laminate. Delamination is a failure mode present in most of the damaged structures and can be ruinous, considering that, the evolution of interlaminar defects can carry the structure to a total failure followed by its collapse. Different techniques are usually adopted to accurately predict the behavior of damaged structures but, due to the complex nature of failure phenomena, there is not an established pattern. The present research project aims to develop a delamination propagation model to estimate a progressive interlaminar delamination failure in laminated composite materials and to allow the prediction of material\'s degradation due to the delamination phenomenon. Experimental tests assisted by ASTM Standards were performed to determine material\'s parameter, like the strain energy release rate, using GFRPs laminated composites. The delamination propagation model proposed was implemented as subroutines in FORTRAN language (UMAT-User Material Subroutine) with formulations based on the Fracture Mechanics. Finally, the model was compiled beside with the commercial Finite Element program ABAQUSTM. / O emprego de materiais compósitos na indústria aeroespacial tem sido gradualmente utilizado devido às suas características fundamentais, como peso leve e alta rigidez, que este tipo de material oferece. Tanto a ciência do material como o desenvolvimento tecnológico que se tem logrado, possibilitaram que estes materiais cumprissem com os requisitos de desempenho para aplicações em estruturas aeronáuticas e aeroespaciais, por tanto, o desenvolvimento de elementos de estruturas primárias usando materiais compósitos, passou a ser muito conveniente. É de extrema importância prestar atenção aos modos de falha que comprometem a performance dos materiais compósitos, uma vez que, estas falhas levam a uma perda de resistência e rigidez do laminado. A delaminação é um modo de falha presente na maioria de estruturas danificadas e pode ser desastroso, considerando que, a evolução dos defeitos interlaminares podem levar a estrutura a falhar seguido pelo colapso estructural. Diferentes técnicas são geralmente adotadas para prever, de maneira correta, o comportamento de estruturas danificadas, porém, devido à natureza complexa do fenômeno de falha, não existe um padrão estabelecido. O presente trabalho de pesquisa visa desenvolver um modelo de delaminação e de propagação da delaminação para estimar a evolução da falha interlaminar em materiais compósitos laminados e permitir a predição do comportamento do material com a evolução da delaminação. Ensaios experimentais auxiliados por normas ASTM foram realizados para determinar parâmetros do material, tais como, as taxas de liberação de energia de deformação, usando materiais compósitos laminados de matriz polimérica reforçada com fibra de vidro. O modelo de propagação da delaminação proposto, foi implementado como uma sub-rotina em linguagem FORTRAN (UMAT – User Material) com formulações baseadas na Mecânica da Fratura. Finalmente, o modelo foi compilado com o software comercial de Elementos Finitos, ABAQUSTM.

Abstract not available

Abstract not available

The high stiffness to weight ratio and fatigue resistance make carbon fibre composites suitable for both military and large civil aircraft. The limited ability of current numerical methods to capture the complex growth of damage in laminated composites leads to a conservative design approach applied in today??s composite aircraft structures. The aim of the presented research was to develop an improved methodology for the failure prediction of laminated composites containing delaminations located between arbitrary layers in the laminate, and to extend the investigations to composite structures subjected to barely visible impact damage (BVID). The advantages of fracture mechanics-based methodologies to predict interlaminar failure in composite structures were identified, from which the crack tip element (CTE) approach and the virtual crack closure technique (VCCT) were selected for assessment. Extensive validation of these fracture mechanics methods is presented on a number of composite structures ranging from coupons to large stiffened panels. It was shown that the VCCT was relatively insensitive to the crack front mesh size, whilst predictions using the CTE methodology were significantly influenced by the element size. Based on the obtained results modelling guidelines for the VCCT and CTE were established. Significant contribution of this research to the field of the analysis of composite structures was the development of a novel test method for the evaluation of embedded single and multi-level delaminations. The test procedure of the single delamination specimen was proposed as an analogous test to conventional compression experiments. The transverse test overcame the inherent problems of in-plane compression testing and produced less scatter of experimental measurements. Quantitative analysis of numerical results employing the validated finite element modelling approaches showed that the failure load and location were in agreement with experiments. Furthermore, new modelling techniques for composite structures containing BVID proposed in this research produced good correlation with test data from the compression after impact (CAI) test. The study of BVID provided a significant contribution toward the knowledge of the applicability of implicit FE solvers to predict failure of CAI specimens as well as the criticality of centrally impacted specimens.

Fatigue assessments have been carried out predominantly with quasi-deterministic approaches, such as the use of SN curves. However, both the loading and the resistance of fatigue prone components are subjected to significant uncertainties. Consequently, a prediction of the remaining fatigue life based on deterministic load and resistance models can lead to unreliable results. This work presents a general reliability-based approach to predict fatigue life of steel components. The approach incorporates prediction of fatigue crack initiation, modeled with a strain-based correlation approach, and propagation, modeled using a linear elastic fracture mechanics approach, and is applicable to new, cracked or repaired structural components. Based on the analysis of existing test results and additional crack initiation and propagation tests on weld metal, the relevant probabilistic fatigue material properties of grade 350WT steel and a matching weld metal were established. An experimental program was carried out on welded details tested either in the as-welded, stress-relieved, conventionally peened, or ultrasonically peened condition. It was demonstrated that ultrasonic peening is superior to the other investigated post weld treatment methods. Using finite element analyses, the results of the tests were deterministically predicted for several different initial conditions, including initial flaw and crack sizes and locations, as well as different levels of residual stresses. A model incorporating an initial flaw and accounting for crack closure and the threshold stress intensity factor range was retained. A probabilistic analysis using Monte Carlo Simulation was carried out to calibrate the relevant parameters. A general reliability-based approach, which includes both the loading and resistance sides of the limit state function was proposed and applied to three practical examples: prediction of test results from two test programs and the prediction of the remaining fatigue life of a cracked component as a function of the safety index. These three applications demonstrated that accurate fatigue life predictions targeting a predefined safety index are achieved. / Structural Engineering

The cyclic-compression behavior of a Cu45Zr45Al5Ag5 bulk metallic glass (BMG) was investigated in order to elucidate the damage initiation and growth mechanisms. The present Cu45Zr45Al5Ag5 BMG was found to have the highest fatigue-endurance limit for BMGs reported to date. Fracture under cyclic compression occurred in a pure shear mode. In addition to many shear bands and cracks, areas of “chipping” were commonly found on the outside surfaces of the fatigue specimens. Crack growth rates were found decrease with cycles. The effects of the as-cast specimen size, cooling rate, and the free volume content on the monotonic and cyclic compression behavior of a Zr-based BMG was investigated. The smaller samples experienced a faster cooling rate, resulting in a higher free volume content. The smaller samples displayed superior monotonic compression and cyclic compression properties. This trend was attributed to a higher free volume content. The effect of the sample aspect ratio (height/diameter) on the cyclic compression behavior of a Zr-based BMG was explored. For smaller aspect ratios (0.5), the yield strength and compressive plastic strain significantly increased when compared to that for an aspect ratio of 2. In general, when the aspect ratio was 0.5, the fatigue lives were longer than when the aspect ratio was 2. The dramatic effect of the sample aspect ratio was attributed to the development of a hydrostatic stress state from the interaction of the uniaxial applied load and the friction stress developed at the interface of the top and bottom specimen surfaces and the platens. The stress-life fatigue behavior and fracture morphology of a (Cu60Zr30Ti10)99Sn1 BMG alloy was investigated under both 3-point and 4-point bending conditions. For all stress levels tested, the fatigue lifetimes tended to be higher for the 3-point loading condition. All fracture surfaces were found to be comprised of four main regions: a crack-initiation site, a stable crack-growth region, an unstable fast-fracture region, and a melting region. Finely spaced parallel marks oriented somewhat perpendicular to the direction of crack propagation were observed in the stable crack-growth region. Analyses of these marks found that their spacing increased with increasing stress intensity- factor range.