Rozprawy doktorskie na temat „Crack tip element”

Thesis (Ph. D.)--Ohio State University, 2003.<br>Title from first page of PDF file. Document formatted into pages; contains xxviii, 314 p.; also includes graphics (some col.) Includes bibliographical references (p. 303-314). Available online via OhioLINK's ETD Center

The main goal of this work is the comparison of the size of the plastic zone at the crack tip for two analysis methods: an analytical linear method and an elastic-plastic analysis employing the Finite Element method (ANSYS software). All calculations were made for a crack loaded under pure shear modes. These types of loading are not sufficiently described in the literature. The first part of this work introduces the problem with the crack tip plastic zone using both linear and nonlinear fracture parameters. The second part is dedicated to the construction of the Finite Element model in the ANSYS software. The geometry of the samples and the loading levels were chosen to match an existing experimental test of the impact of shear modes on the crack behavior. In the third part of this thesis, the plastic zone radii for pure shear modes II and III are estimated using several methods and the results are compared. In the last part of this work, the same procedure as in the previous part is applied on a mixed-mode II+III loading. A result of this thesis is the assessment of the application limits of the linear analysis method used to estimate the size of the plastic zone at the crack tip for a specific geometry and material model.

This dissertation proposes hybrid models for (i) diagnosis and (ii) remaining useful life estimation of a single fatigue crack in a low-pressure turbine blade. The proposed hybrid methods consist of physics-based methods and data-driven methods. In this dissertation, blade tip timing is used to measure the relative tip displacement of a rotor blade. The natural frequency of the blade is determined by detecting the critical speeds of the blade using a newly derived least squares spectral analysis method. The method shares its origin from the Lomb-Scargle periodogram and can detect resonance frequencies in the blade’s displacement while the rotor is in operation. A Campbell diagram is then used to convert the critical speed into a natural frequency. Two kinds of shaft transients are considered, a run-up run-down crossing the same critical speed, is used to test the new method. This dissertation shows that the relative displacement of the blade tip is comparable to those simulated from an analytical single degree of freedom model. It is also shown that the newly proposed resonance detection method estimates the natural frequency of the blade to a high degree of accuracy when compared to the measurements from a modal impact hammer test. The natural frequency obtained from the real time measurement is then used in a pre-constructed hybrid diagnostics model. The diagnostics model provides a probability density function estimation of the surface crack length given the measured natural frequency. A Gaussian Process Regression model is trained on data collected during experiments and finite element simulations of a fatigue crack in the blade. The final part of this dissertation is a sequential inference model for improving the estimation of the crack length and the prediction of the crack growth. The suggested model uses an unscented Kalman filter that improves estimations of the crack length and the rate of crack growth from Paris’ Law coefficients. The model is updated each time a diagnosis is performed on the blade. The RUL of the blade is then determined from an integration of Paris’s Law given the uncertainty estimates of the current damage in the blade. The result of the algorithm is an estimation of the remaining number of cycles to failure. The algorithm is shown to improve the overall estimation of the RUL; however, it is suggested that future work looks at the convergence rate of the method.<br>Dissertation (MEng)--University of Pretoria, 2019.<br>Eskom Power Plant Engineering Institute (EPPEI)<br>Mechanical and Aeronautical Engineering<br>MEng<br>Unrestricted

Sous l’effet des impacts mécaniques, les structures constituées de matériaux fragiles peuvent être exposés à la rupture dynamique. La modélisation appropriée des mécanismes de rupture à différentes échelles d’observation et la prédiction de l’endommagement thermomécanique dans ces matériaux sont essentielles pour la conception de structures fiables. Des observations expérimentales sur la rupture dynamique des matériaux fragiles montrent des effets de refroidissement et d’échauffement importants à proximité d’une pointe de fissure. La modélisation du couplage thermomécanique lors de la rupture fragile a été entreprise, en général, sans tenir compte des aspects microstructuraux. L’objectif de cette thèse est de développer une procédure pour obtenir des lois d’endommagement thermomécaniques dans lesquelles l’évolution de l’endommagement est déduite à partir de la propagation des microfissures et des effets thermiques associés à l’échelle petite du matériau. Nous utilisons la méthode d’homogénéisation asymptotique pour obtenir la réponse macroscopique thermomécanique et d’endommagement du solide. Pour la propagation des microfissures, en mode I ou II, un critère de type Griffith est adopté. Des sources de chaleur sont considérés aux pointes des microfissures en mouvement, en lien avec l’énergie dissipée pendant la propagation. Nous considérons aussi des sources de chaleur représentant la dissipation par frottement sur les lèvres des microfissures qui se propagent en mode de cisaillement. Grâce à une analyse énergétique combinée avec la méthode d’homogénéisation nous obtenons des lois d’endommagement macroscopiques. Dans le système thermoélastique et d’endommagement ainsi obtenu, on identifie de forts couplages entre les champs mécaniques et thermiques. Le calcul des coefficients effectifs nous a permis d’étudier la réponse locale prédite par les nouveaux modèles. Cette réponse montre des effets de vitesse de déformation, de taille de la microstructure, de dégradation des propriétés thermoélastiques et des évolutions thermiques spécifiques engendrées par la microfissuration et le frottement à l’échelle petite du matériau. Dans l’équation macroscopique de la température, on retrouve des termes sources de chaleur distribuées en lien avec les dissipations d’endommagement et de frottement. L’implémentation de modèles d’endommagement dans un logiciel d’éléments finis nous a permis d’effectuer des simulations numériques à l’échelle des structures. Nous avons reproduit numériquement certains tests expérimentaux publiés dans la littérature concernant la rupture rapide d’échantillons de PMMA sous sollicitation d’impact. Les résultats des simulations obtenus sont en bon accord avec les observations expérimentales<br>Under impact mechanical loadings, structural components made of brittle materials may be exposed to dynamic failure. The appropriate modeling of the failure mechanisms at different scales of observation and the prediction of the corresponding thermomechanical damage evolution in such materials is essential for structural reliability predictions. Experimental observations on dynamic failure in brittle materials report important cooling and heating effects in the vicinity of the crack tip. Theoretical modeling of the thermo-mechanical coupling during fracture have been generally undertaken without accounting for microstructural aspects. The objective of the present thesis is to develop a procedure to obtain macroscopic thermo-mechanical damage laws in which the damage evolution is deduced from the propagation of microcracks and the associated small-scale thermal effects in the material. We use the asymptotic homogenization method to obtain the macroscopic thermo-mechanical and damage response of the solid. A Griffith type criterion is assumed for microcracks propagating in modes I or II. Heat sources at the tips of microcracks are considered as a consequence of the energy dissipated during propagation. Frictional heating effects are also considered on the lips of microcracks evolving in the shear mode. An energy approach is developed in combination with the homogenization procedure to obtain macroscopic damage laws. The resulting thermoelastic and damage system involves strong couplings between mechanical and thermal fields. Computation of the effective coefficients allowed us to study the local response predicted by the new models. The macroscopic response exhibits strain-rate sensitivity, microstructural size effects, degradation of thermoelastic properties and specific thermal evolutions due to microcracking and frictional effects at the small scale. Distributed heat sources are present in the macroscopic temperature equation linked to damage and frictional dissipations. The implementation of the proposed damage models in a FEM software allowed us to perform numerical simulations at the structural level. We reproduced numerically experimental tests reported in the literature concerning the rapid failure of PMMA samples impact. The results obtained in the simulations are in good agreement with the experimental observations

碩士<br>淡江大學<br>機械工程學系<br>89<br>In this thesis a special crack tip element has been developed in which displacements and stresses have same behavior as those of bi-material interface cracks with open tips. As the crack is along an interface of materials with identical elastic moduli, the element degenerates into a traditional quarter point element. By using the isoparametric coordinate system specified in this thesis, element stiffness matrices may be easily calculated. Also, it is shown in this study the complex may be obtained. Numerical results are in good agreement with known analytical solutions in two examples.

碩士<br>國立成功大學<br>機械工程學系碩博士班<br>90<br>Abstract The purpose of this research is to study the effect of higher order elements in solving the crack tip stress intensity factor (SIF), and to compare the results with those obtained by using the singular elements. We also study the positions of the superconvergent points as well as the method of static condensation beforehand. In energy norm,the n-th order Lagrange elements have the superconvergent rate with the order of n+1,and their locations are on n by n Gauss integration points. The accuracy and convergent rate of the Lagrange elements are better than the other two kinds of elements which are Serendipity and Enriched Serendipity. The method which using the static condensation in solving process will save a large amount of time with lager and lager degrees of freedom especially. When using the method of displacement extrapolation to solve SIF, we find that the second order interpolation method seems to be more reasonable than the first order one.Singular elements have the better approximate results than higher order elements with the problems of the singularity equaling to 1/sqrt(r), especially in the case of using triangular singular elements. But the higher order elements also have satisfying results (the error less than 1% ). For the problem of the same total degrees of freedom,the higher order elements spend less time and have better accuracy than lower order elements, if these higher order ones can collocate the method of static condensation in solving process. keywords : finite element method,superconvergent rate, higher order elements, displacement extrapolation method,stress intensity factor, static condensation

博士<br>國立成功大學<br>土木工程學系<br>103<br>Generally speaking, the stress in crack and notch tip will produce infinitely great phenomenon. For the two-dimensional crack and notch problems, stress near the crack and notch tip can solved exactly by the theoretical analysis, but for the three-dimensional crack and notch ones, for example a plate with a notch, there is no rational solutions at present. In this thesis, the element-free method will be used to solve the mechanics problem of crack and notch, and the main reason is that the element-free method can add stress and strain functions in the strength matrix easily. The element-free method has a wild application on crack problem, but there are no relevant documents using this method on the notch mechanics problem at present. First, the basic theory of the element-free method will be further extended to solve the numerical problems associated with this method in this thesis. Second, the theoretical formula will be used to derive the stress and displacement fields on in-plan notch problems with anisotropic materials, and then this theory results will be applied to the element-free method. Finally, a singularity notch element is set up in this thesis, and this method can obtain more accurate analysis result with the node that is relatively dredged. Furthermore, this thesis proposes the theoretical solution for the three-dimensional problem containing a semi-infinite crack with primary and shadow solutions, where the primary solution is the traditional plane-strain solution and the shadow ones can be obtained from the 3D equilibrium equation of the theory of elasticity. A least-squares method incorporating the finite element results was used to determine these factors in this theoretical solution. The results of this research show that if enough primary and shadow solutions are included, numerical simulations indicate that the proposed method can obtain an accurate displacement field for 3D crack problems. The major advantage of this method is that a 3D whole displacement field with the analytic singular effect near the crack tip can be obtained, without any limitation with regard to the material properties, boundary conditions, and applied loads. Finally, the element-free method is applied to the three-dimensional fracture mechanics preliminarily, and the result was compared with the normal finite element method result using a fine mesh. The major advantage is that the crack stress singularity, which is ignored in the finite element method, can be obtained in the proposed method.

The objective of this thesis is to study the fracture behavior of bulk metallic glasses. For this purpose, detailed finite element investigation of the mode I and mixed mode (I and II) stationary crack tip fields under plane strain, small scale yielding conditions is carried out. An implicit backward Euler finite element implementation of the Anand and Su constitutive model [Anand, L. and Su, C., 2005, J. Mech. Phys. Solids 53, 1362] is used in the simulations. The effects of internal friction (μ), strain softening, Poisson's ratio (ν) and elastic mode mixity (Me) on the near-tip stress and deformation fields are examined. The results show that under mode I loading, a higher μ leads to a larger normalized plastic zone size and higher plastic strain level near the notch tip, but causes a substantial decrease in the opening stress. The brittle crack trajectories and shear band patterns around the notch are also simulated. An increase in ν reduces the extent of plastic zone and plastic strain levels in front of the notch tip. The results from mixed mode simulations show that increase in the mode II component of loading dramatically increases the maximum plastic zone extent, lowers the stresses and significantly enhances the plastic strain levels near the notch tip. Higher μ causes the peak magnitudes of tensile tangential stress to decrease. The implications of the above results on the fracture response of bulk metallic glasses are discussed. The possible variations of fracture toughness with mode mixity predicted by employing two simple fracture criteria are examined. Finally, mixed mode (I and II) fracture experiments on a Zr-based bulk metallic glass are performed. It is found that the fracture toughness increases with Me and Jc under mode I is higher than that under mode II loading by a factor of 4. The operative failure mechanism and fracture process zone size are discerned based on observations of incipient crack growth and fractographs. Lastly, a fracture criterion is proposed which predicts the experimentally observed variation of fracture toughness with mode mixity.

The large plastic deformations at the tip of a crack in a ductile heat treatment of 4340 steel are studied experimentally and numerically to investigate the details of the deformation in a tough material. The specimen is loaded in a three-point-bend arrangement. The finite-element model of the experiment uses a small-strain, incremental plasticity law, with a power-law hardening behavior. Both the in-plane and out-of-plane deformations were measured on the same specimen at the same time. The experimental technique of moire interferometry is used to measure the in-plane displacements. This technique is described in detail, including an analysis of the effect of out-of-plane rotations on the use of the technique. A four-beam interferometer for measuring orthogonal displacement components is described, and its performance analyzed. The three-dimensional, finite-element model has 11913 degrees of freedom, and provides data for comparison with the experiment between 4000 N (linear behavior) up to 73.5 kN (continuous fracture of the steel specimen). The model material properties are determined from a uniaxial test on specimens taken from the same bar as the fracture specimens and with identical heat treatment. This model characterizes the crack as a rounded notch to match the notch in the steel fracture specimen. The effects of tunneling of the crack are introduced through the release of nodes along the crack plane corresponding to measured crack profiles. Results indicate that the numerical model matches the experiment quite well up to a load of 52.3 kN; mismatch at higher loads may be caused by a lack of finite-strain formulation in the code. The finite notch tip negates the singularity in either the stress or strain fields; the HRR field seems to have no region of dominance. However, the function of the J-integral appropriate to the HRR field does normalize the stresses and strains well, indicating that the J-integral is still a good fracture criterion. The effects of the added tunnel indicate that failure of the material depends on both the plastic strain and the hydrostatic stress.

Double cantilever beam (DCB) specimens with distinct intermetallic microstructures and different geometries were fractured under different mode ratios of loading, ψ, to obtain critical strain energy release rate, Jc. The strain energy release rate at crack initiation, Jci, increased with phase angle, ψ, but remained unaffected by the joint geometry. However, the steady-state energy release rate, Jcs, increased with the solder layer thickness. Also, both the Jci and Jcs decreased with the thickness of the intermetallic compound layer. Next, mode I and mixed-mode fracture tests were performed on discrete (l=2 mm and l=5 mm) solder joints arranged in a linear array between two copper bars to evaluate the J = Jci (ψ) failure criteria using finite element analysis. Failure loads of both the discrete joints and the joints in commercial electronic assemblies were predicted reasonably well using the Jci from the continuous DCBs. In addition, the mode-I fracture of the discrete joints was simulated with a cohesive zone model which predicted reasonably well not only the fracture loads but also the overall load-displacement behavior of the specimen. Additionally, the Jci calculated from FEA were verified estimated from measured crack opening displacements in both the continuous and discrete joints. Finally, the pad-crater fracture mode of solder joints was characterized in terms of the Jci measured at various mode ratios, ψ. Specimens were prepared from lead-free chip scale package-PCB assemblies and fractured at low and high loading rates in various bending configurations to generate a range of mode ratios. The specimens tested at low loading rates all failed by pad cratering, while the ones tested at higher loading rates fractured in the brittle intermetallic layer of the solder. The Jci of pad cratering increased with the phase angle, ψ, but was independent of surface finish and reflow profile. The generality of the J =Jci(ψ) failure criterion to predict pad cratering fracture was then demonstrated by predicting the fracture loads of single lap-shear specimens made from the same assemblies.