Computational dynamic fracture mechanics

This paper provides a review on the state of the art in computational dynamic fracture mechanics. The following important essential ingredients in computational dynamic fracture mechanics are included: (i) fundamental aspects of dynamic fracture mechanics, (ii) types of fracture simulation, (iii) computational models of dynamic crack propagation, and (iv) use of dynamic J-integral in computational models. In the item (i), a special attention is focused on the asymptotic eigen fields for various states of dynamic crack tips, which provide the foundation of dynamic fracture mechanics as Williams' asymptotic eigen solutions provided the foundation of static linear fracture mechanics. In the item (ii), a new concept of mixed-phase simulation is presented for general nonself-similar crack propagation, in addition to the generation-phase and application-phase simulations. A comprehensive summary of computational models for dynamic crack propagation is given in the item (iii). Finally, in the item (iv) several attractive features of the dynamic J-integral are presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Some considerations on dynamic biem—II: Applications to two-dimensional fracture mechanics problems

Part I of this report, published in a detached part, the theoretical and numerical fundamentals of BIEM techniques in dynamic were presented.In Part II, numerical results for input problems obtained by BIEM, through a dynamic program of general applications, are shown.     

An expert system approach to fracture mechanics

The usefulness of an arificial intelligence approach to some deterministic problems is discussed. An expert system approach to fracture mechanics problems is devised. Production rules for a simple expert system for crack tip mesh mapping are given. The knowledge acquisition process described in the references is used. Linear 2D fracture problems can be solved by the given program, though the methodology would be similar for non-linear or 3D problems.     

Method of singular integrodifferential equations in plane dynamic problems of fracture mechanics

We develop a method for the solution of two-dimensional dynamic problems of the theory of elasticity for infinite bodies with smooth curvilinear cracks combining a modified method of finite differences in time with the method of singular integrodifferential equations in the space variables. Integral representations of the wave potentials are constructed and used to reduce the first boundary-value problem to the solution of systems of integrodifferential equations by the method of mechanical quadratures. The time dependences of the computed dynamic stress intensity factors at the tips of a rectilinear crack are analyzed for various impact and pulsed loads acting upon the crack lips.     

From continuum mechanics to fracture mechanics: the strong discontinuity approach

The paper deals with the strong discontinuity approach and shows the links with the decohesive fracture mechanics provided by that approach. On the basis of 1D continuum damage models it is shown that, by introducing some few ingredients like the strong discontinuity kinematics, discrete constitutive models (traction vs. displacement jumps) are automatically induced. For the general 2D-3D cases it is shown that the weak discontinuity concept is an additional ingredient, necessary in order to fulfill the strong discontinuity conditions, which allows to establish additional links with the fracture process zone concept. Also classical fracture mechanics properties as the fracture energy are related to the continuum model properties in a straightforward manner.     

A fracture mechanics approach to ceramo-metal bond evaluation

The incidence of mechanical failure of cast metal/porcelain dental restorations has promoted a study to develop reliable methods of characterizing and improving bond strengths when produced under standard dental laboratory conditions. Single-edge notch beam specimens were prepared by firing porcelain from a single blended frit to either side of a central metal coupon and subjecting these to four-point bending at 20 ± 2° C and 0.5 mm min^–1 crosshead speed. Specimens of three representative dental alloys and an experimental alloy were prepared in two specimen sizes and three notch widths. The fracture toughness (K _Ic) values were independent of notch width and specimen size over the range of these variables examined and good discrimination was obtained. The fracture toughness of all bonds was improved by a commercial hot isostatic pressure cycle. SEM examination of the fractured surfaces suggested that this improvement was due to the reduction in microporosity at the interface.     

An internal variable approach to elastic-plastic fracture mechanics

An internal variable approach to the modelling of a cracked element is suggested. As well as providing an alternative failure criterion, the internal variable formulation treats elastic-plastic (or ductile) fracture as a structural problem, allowing the distinction to be made between fixed displacement and fixed loading conditions. Crack growth in a cracked elastic-plastic plate is determined for a particular form of the limit surface, and a simple criterion for stability emerges.     

Some considerations on dynamic biem—I: A dynamic program for two-dimensional fracture mechanics problems

In Part I of this report, the theoretical and numerical fundamentals of BIEM techniques in real transformed dynamic are presented.Interesting remarks on how the numerical integrations have been done, are pointed out in the method.In Part II, to be published in a detailed paper, numerical results for impact problems obtained by BIE Method, through a dynamic program of general application, will be shown.     

Numerical studies in dynamic fracture mechanics

This paper provides a summary of recent studies concerning numerical modeling of dynamic crack-propagation, Both stationary mesh as well as moving mesh finite-element procedures are examined. Simple procedures, using a moving mesh of conventional isoparametric elements in conjunction with certain path-independent integrals for the evaluation of stress-intensity factors for a dynamically propagating crack are presented.

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Résumé Le mémoire fournit des synthèses des études récentes relatives à la modélisation numérique de la propagation de fissures dynamiques. On examine, à la fois, le maillage stationaire et le maillage mobile utilisés dans les procédures d'éléments finis. On présente des procédures simples utilisant un maillage mobile d'éléments conventionnels isoparamétriques utilisé avec certaines intégrales indépendantes du parcours, en vue d'évaluer les facteurs d'intensité de contrainte dans le cas d'une fissure en cours de propagation dynamique.

     

Application of fiber optic sensors to fracture mechanics problems

An experimental study is conducted to show the application of fiber optic sensors to fracture mechanics problems. Mode I stress intensity factors are obtained using single mode optical fibers in single edge notched specimens fabricated from aluminium. A Mach–Zehnder interferometric set up is used during the experiments. The experimental results compare well with theoretical predictions.     

Some problems in experimental fracture mechanics

A standard procedure for the determination of fracture toughness K_IC is discussed. The insufficiency of the existing K_ic determination confidence criteria is stressed and the following criteria are proposed instead: φ_max ? 1.5%; $\text{σ}{}_{\mathrm{fr}}{}^{\mathrm{net}}\text{σ}{}_{\mathrm{0.2\; ?\; 0.8}}$, in conjunction with the old criterion $\text{P}{}_{\max }\text{P}{}_{\mathrm{Q}}\text{? 1.1}$. Determination of K_IC from P_max should be used instead of from P_Q.A method for the determination of a point on the “force-displacement” diagram corresponding to crack growth initiation is set forth. The method is based on specimen compliance tests under repeated load-relief cycles. The crack growth initiation point is used to determine both the critical crack opening and plane strain fracture toughness. The indefinite effect of the growing crack (in the ease of crack opening or Cherepanov-Rice integral calculations) is thereby eliminated. Necessity is emphasized to determine the share of the J-integral which contributes to fracture process. A method for plotting the elastic displacement diagram is proposed which allows on the basis of preliminary estimates to determine fracture toughness of small-sized specimens without using special setups. The area ratio between the plastic and elastic strain diagrams is proposed to be adopted as fracture type criterion. Certain experiments to determine crack resistance of material specimens are described and discussed.     

A synergistic fracture mechanics approach to fatigue life evaluation

A technique for modeling synergistic effects in fatigue crack propagation (FCP) is presented. First, a mission (load/temperature history) is segregated into elemental damage events. A simple three parameter model is then used to describe these events. The model coefficients are seen to be interrelated linear functions of FCP rate controlling variables such as frequency, temperature, stress ratio (σ_min/σ_max), dwell, overload ratio ($\text{P}{}_{\mathrm{overload}}$/$\text{P}{}_{\max }$) and cycles between overload. Finally, integrating event-by-event crack advance gives the expected component crack propagation life under mission cycling. Results of this procedure applied to gas turbine disk materials IN100 and Waspaloy are discussed to examine the accuracy of the model.     

Dual approach in non-linear fracture mechanics

A dual approach in fracture mechanics based on complementary energy is proposed. The analysis of the dissipation shows that the thermodynamical force associated with the evolution of a crack is an energy release rate, form of which depends on the presence or not of mechanical discontinuities. This energy release rate is given as a integral based on free or complementary energy. The invariance of sintegrals is analysed and the obtained results in elastoplasticity are discussed. The energy release rate is determined in terms of potential energy or complementary energy, first in elasticity and secondly in elastoplasticity. Associated to these definitions, the law of propagation of the crack is chosen as a Griffith law and the propagation is governed by a normality rule. In this framework we formulate the evolution problem concerning crack propagation in an elastoplastic material. Variational formulations are obtained in terms of rate of displacement, of stresses and of crack length.     

Elastodynamic parameters for dynamic interface fracture mechanics

Summary Dynamic extension of cracks running along curvilinear interfaces of brittle bimaterials subjected to mechanical crack surface loads and superimposed thermal strains acting along the ligament is considered. This paper especially addresses the provision and discussion of elastodynamic interface parameters in order to assess quantitatively the bimaterial fracture in view of the governing physical features: applied mechanical and thermal strain loading, existence of an interface, crack-tip velocity and curvature of the interface contour. By utilizing the linear theory of thermoelasticity and adopting Stroh's method of generalized complex potentials, from the corresponding boundary and continuity conditions vectorial Hilbert problems are derived. It is shown that the parameters of the eigenvalues and of the eigenvectors of the Hilbert problems can be interpreted as elastodynamic interface mechanics parameters reading (,v _p, _Hf , _Hf ). Generalized Dundurs parameters of dynamics (, ) and consequently an associated generalized Dundurs diagram of dynamics are proposed. While the aforementioned elastodynamic interface parameters (, ,v _p, _Hf , _Hf ) do not assume the interface to be damaged, interfaces with running interface cracks generally cause two additional interface parameters, denoted as bimaterial constants (, _Hf ), where the latter is specific to the curvature of the interface in conjunction with the velocity of the interface crack. However, the bimaterial constants (, _Hf ) can be traced back to interface parameters for an uncracked bimaterial, namely to (, _Hf ).