It is known that the classical inverse square root singularity used in Linear Elastic Fracture Mechanics (LEFM) is lost as a crack intersects a stress free surface. As a result, the stress and displacement equations are given as eigenvalue series expansions, with the lowest order eigenvalue dominating the series. The thickness averaged stress and surface displacement singularity exponents were determined for a commercially available polyurethane. Multiple specimen geometries were used to “benchmark” the optical methods. Tests have been run to determine the surface effect on a straight front crack. Results of these tests were compared with analytical results and related to LEFM concepts. / Master of Science

Este trabalho visa modelar e estabelecer procedimentos experimentais para permitir a construção de mapas de conformabilidade plástica dos metais fundamentados na mecânica da fratura não-linear elasto-plástica. Um critério de conformabilidade plástica foi desenvolvido pela utilização de uma integral invariante generalizada baseada no teorema de Noether das integrais invariantes. Discute-se também as limitações da teoria da plasticidade que impossibilitam a obtenção de critérios de conformabilidade por seu intermédio. É um importante objetivo proporcionar o surgimento de uma metodologia de ensaio contendo alto rigor técnico mas sendo de baixo custo e de fácil implementação em simples instalações industriais. O procedimento foi aplicado no estudo do caso do forjamento a frio em matriz aberta, simulado por ensaio de compressão em prensa hidráulica. / The present study is aimed to the development of a low cost, to be implemented with ease, and technicality satisfactory industrial type testing for metal forming workability analysis. It is concerned with the development of an experimental procedures to permit the building up the metal forming workability maps, based on the nonlinear elastic-plastic fracture mechanics. A generalized nonlinear fracture mechanics invariant integral was applied to the case problem of the cold forging in flat open die of a ductile metallic material. At end a fracture criterion was developed in order to be possible the construction of the fracture deformation maps of the case study.

This work describes the implementation of the eXtended Finite Element Method (XFEM) in the Abaqus software package. A user-defined element was developed containing the analytical functions relating to homogeneous and interface fracture mechanics. The long-term goal of such work is to increase the ability to analyze fractures and other imperfections in multimaterial systems containing large elastic mismatches, such as flexible electronics. A review of XFEM-related literature is presented, as well as an overview of fracture mechanics for both homogeneous and interface systems. The theoretical basis of the XFEM is then covered, including the concepts of Partition of Unity and stress intensity factor evaluation. Finally, numerical results of the implementation are compared to several benchmark cases, along with conclusions and suggestions for future work.

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This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / Thesis: Ph. D., Massachusetts Institute of Technology, Department of Earth and Planetary Science, 1977 / Vita. / Bibliography : leaves 135-137. / By Robert Wayne Siegfried, II. / Ph. D. / Ph. D. Massachusetts Institute of Technology, Department of Earth and Planetary Science

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The thesis presents novel formulations of hereditary cohesive zone models able to capture rate-dependent crack propagation along a defined interface. The formulations rely on the assumption that the measured fracture energy is the sum of an intrinsic fracture energy, related to the rupture of primary bonds at the atomic or molecular level, and an additional dissipation caused by any irreversible mechanisms present in the material and occurring simultaneously to fracture. The first contribution can be accounted for by introducing damage-type internal variables, which are to be driven by a rateindependent evolution law in order to be coherent with the definition as intrinsic energy. It is then proposed that the additional dissipation can be satisfactorily characterised by the same continuum-type material constitutive law obeyed by the interface material considered as a continuum: it is postulated that the dimensional reduction whereby a three-dimensional thin layer is idealized as a surface does not qualitatively alter the functional description of the free energy. The specific application considered is mode-I crack propagation along a rubber interface. After focusing on viscoelasticity as a suitable candidate to reproduce rubber’s behaviour, firstly the most common relaxation function, namely a single exponential term, is considerd after which the attention is turned to the use of fractional calculus and the related fractional integral kernel. A comparison with experimental results is presented. A shortcoming of the proposed approach is then noted, in that certain features of experimentally measured responses (i.e.the non-monotonicity of the critical energy-release rate with respect to crack speed) will be shown to be out of reach for the described modelling paradigm. A novel micromechanical formulation is then sketched in an attempt to qualitatively understand the phenomenon. An additional interface damaging mode is introduced, physically inspired by the desire to reproduce the formation of fibrils in a neighbourhood of the crack tip. Fibril formation is then driven by a variational argument applied to the whole of the interface, yielding its non-local character. Upon the introduction of an anisotropic fracture energy, motivated by experimental considerations, it is noted how the model can predict a non-monotonic energy-release rate vs crack speed behaviour, at least for a simple loading mode.

The use of classical creep continuum damage mechanics, constitutive and damage equations is restricted, to model certain types of creep deformation and fracture mechanisms, under isothermal conditions; and, to extend their predictive capabilities for a wider range of problems they have to be modified. The constitutive and damage equations are modified to represent the bi-linear, log. stress vs. log. rupture, and the log, stress vs. minimum strain rate, characteristics of materials; so that the change in material behaviour, as a mechanism change occurs, is represented in the constitutive model, by a change in the slope of these characteristic lines. Uni-axial creep tests of as-cast (OFHC) Copper have been performed at 150°C, 250°C and 500°C; and, an anisothermal constitutive model has been developed for the temperature range 150°C to 500°C, which highlights how the constitutive equations may be modified, to model creep behaviour under varying temperature conditions. The model predictions are in good agreement with the test results. A compact tension specimen has been studied, which has shown the importance of modelling the effects on rupture, of the high tri-axial stress-state present at the crack-tip, which accelerates void growth. Modified constitutive equations, have been used to model the mechanism of constrained cavity growth, and has enabled improved damage distribution and. lifetime predictions to be obtained for the compact tension specimen, similar to those expected from experimental tests. Non-local damage techniques are developed to model the effects of grain size characteristic dimension, on the failure of large and small cracked tension specimens. Non-local damage techniques are shown to be necessary to give accurate, physically related, finite element solutions. Suitably modified constitutive and damage rate equations are used to model the high temperature failure of a circumferential weld, in a thick steam-pipe, operating at a constant temperature and pressure. The models developed predict, the growth of damage in certain microstructural regions of the weld, and the lifetime of the component; which are observed to be in close agreement with the results from a fullsize pressure vessel tests. It will be shown that it is essential to use creep constitutive and damage equations in computer models, which accurately represent the underlying physics of IX the predominant creep mechanisms present. The implications of the research work on future computer modelling and on design are discussed.

Short crack growth behaviour was studied using a method of plastic replication on hour-glass shaped specimens of a medium carbon steel which were subjected to push-pull fatigue testing at ambient temperature. Crack lengths were measured from replicas using an optical microscope from which the growth rate could be calculated. A theory for short crack growth is presented which may be expressed mathematically by the equation:- = (for a < d) da dN where (a) is crack length, (d) is a characteristic dimension between adjacent microstructural obstacles to crack propagation, C1 is a function of stress or strain range and a is a constant. For the medium carbon steel used in this study (d) was equated to the ferrite band length which contained the growing crack. This theory was used to model short crack growth in an Aluminium alloy T6-7075 Al and for the medium carbon steel used in this project. iii By using a second equation to describe "long" crack growth of the form:- da dN = where C2 is a function of the applied strain range and 0 is a constant, it was then possible to describe the complete history of crack growth. By obtaining short crack growth data for different stress levels, quantitative expressions of these two equations were calculated from which fatigue lifetime predictions could be made by integration of the equations for any stress level. Using this method an estimate could also be made of the percentage of fatigue lifetime spent in the initiation and growth of short cracks.